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Journal of Fixed Point Theory and Applications最新文献

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Existence of solutions and approximate controllability of second-order stochastic differential systems with Poisson jumps and finite delay 具有泊松跳跃和有限延迟的二阶随机微分系统的解的存在性和近似可控性
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-09-16 DOI: 10.1007/s11784-024-01129-4
Xiaofeng Su, Dongxue Yan, Xianlong Fu
{"title":"Existence of solutions and approximate controllability of second-order stochastic differential systems with Poisson jumps and finite delay","authors":"Xiaofeng Su, Dongxue Yan, Xianlong Fu","doi":"10.1007/s11784-024-01129-4","DOIUrl":"https://doi.org/10.1007/s11784-024-01129-4","url":null,"abstract":"<p>Stochastic differential equations with Poisson jumps become very popular in modeling the phenomena arising in various fields, for instance in financial mathematics, where the jump processes are widely used to describe the asset and commodity price dynamics. The objective of this paper is to investigate the approximate controllability for a class of control systems represented by second-order stochastic differential equations with time delay and Poisson jumps. The main technique is the theory of fundamental solution constructed through Laplace transformation. By employing the so-called resolvent condition, theory of cosine operators and stochastic analysis, we formulate and prove some sufficient conditions for the approximate controllability of the considered system. In the end an example is given and discussed to illustrate the obtained results.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142251768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An integral RB operator 积分 RB 算子
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-09-06 DOI: 10.1007/s11784-024-01125-8
Marvin Jahn, Peter Massopust
{"title":"An integral RB operator","authors":"Marvin Jahn, Peter Massopust","doi":"10.1007/s11784-024-01125-8","DOIUrl":"https://doi.org/10.1007/s11784-024-01125-8","url":null,"abstract":"<p>We introduce the novel concept of integral Read–Bajraktarević (iRB) operator and discuss some of its properties. We show that this iRB operator generalizes the known Read–Bajraktarević (RB) operator and we derive conditions for the fixed point of the iRB operator to belong to certain function spaces.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-09-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142205892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symmetry and monotonicity of positive solutions for a Choquard equation involving the logarithmic Laplacian operator 涉及对数拉普拉斯算子的乔夸尔方程正解的对称性和单调性
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-08-17 DOI: 10.1007/s11784-024-01121-y
Linfen Cao, Xianwen Kang, Zhaohui Dai
{"title":"Symmetry and monotonicity of positive solutions for a Choquard equation involving the logarithmic Laplacian operator","authors":"Linfen Cao, Xianwen Kang, Zhaohui Dai","doi":"10.1007/s11784-024-01121-y","DOIUrl":"https://doi.org/10.1007/s11784-024-01121-y","url":null,"abstract":"<p>In this paper, we study a Schrödinger–Choquard equation involving the logarithmic Laplacian operator in <span>(mathbb {R}^{n})</span>: </p><span>$$begin{aligned} mathcal {L}_triangle u(x)+omega u(x)=C_{n,s}(|x|^{2s-n}*u^{p})u^{r}, xin mathbb {R}^{n}, end{aligned}$$</span><p>where <span>(0&lt;s&lt;1, p&gt;1, r&gt;0, nge 2, omega &gt;0)</span>. Using the direct method of moving planes, we prove that if <i>u</i> satisfies some suitable asymptotic properties, then <i>u</i> must be radially symmetric and monotone decreasing about some point in the whole space. The key ingredients of the proofs are the narrow region principle and decay at infinity theorem; the ideas can be applied to problems involving more general nonlocal operators.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142205893","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Radially symmetric solutions of a nonlinear singular elliptic equation 非线性奇异椭圆方程的径向对称解
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-08-16 DOI: 10.1007/s11784-024-01124-9
Shu-Yu Hsu
{"title":"Radially symmetric solutions of a nonlinear singular elliptic equation","authors":"Shu-Yu Hsu","doi":"10.1007/s11784-024-01124-9","DOIUrl":"https://doi.org/10.1007/s11784-024-01124-9","url":null,"abstract":"<p>For any <span>(lambda ge 0)</span>, <span>(2le nle 4)</span> and <span>(mu _1in mathbb {R})</span>, we will prove the existence of unique radially symmetric solution <span>(hin C^2((0,infty ))cap C^1([0,infty )))</span> for the nonlinear singular elliptic equation <span>(2r^{2}h(r)h_{rr}(r)=(n-1)h(r)(h(r)-1)+rh_r(r)(rh_r(r)-lambda r-(n-1)))</span>, <span>(h(r)&gt;0)</span>, in <span>((0,infty ))</span> satisfying <span>(h(0)=1)</span>, <span>(h_r(0)=mu _1)</span>. We also prove the existence of unique analytic solution of the about equation on <span>([0,infty ))</span> for any <span>(lambda ge 0)</span>, <span>(nge 2)</span> and <span>(mu _1in mathbb {R})</span>. Moreover we will prove the asymptotic behaviour of the solution <i>h</i> for any <span>(nge 2)</span>, <span>(lambda ge 0)</span> and <span>(mu _1in mathbb {R}setminus {0})</span>.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142205891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and asymptotic behavior of solutions for nonhomogeneous Schrödinger–Poisson system with exponential and logarithmic nonlinearities 具有指数和对数非线性的非均质薛定谔-泊松系统解的存在性和渐近行为
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-08-06 DOI: 10.1007/s11784-024-01122-x
Xiaoli Lu, Jing Zhang
{"title":"Existence and asymptotic behavior of solutions for nonhomogeneous Schrödinger–Poisson system with exponential and logarithmic nonlinearities","authors":"Xiaoli Lu, Jing Zhang","doi":"10.1007/s11784-024-01122-x","DOIUrl":"https://doi.org/10.1007/s11784-024-01122-x","url":null,"abstract":"<p>In this paper, we consider the following nonhomogeneous quasilinear Schrödinger–Poisson system with exponential and logarithmic nonlinearities </p><span>$$begin{aligned} left{ begin{array}{ll} -Delta u+phi u =|u|^{p-2}ulog |u|^2 +lambda f(u) +h(x),&amp;{} textrm{in} hspace{5.0pt}Omega , -Delta phi -varepsilon ^4 Delta _4 phi =u^2,&amp;{} textrm{in}hspace{5.0pt}Omega , u=phi =0,&amp;{} textrm{on}hspace{5.0pt}partial Omega , end{array} right. end{aligned}$$</span><p>where <span>(4&lt;p&lt;+infty ,,varepsilon ,,lambda &gt;0)</span> are parameters, <span>(mathrm{Delta _4 phi = div(|nabla phi |^2 nabla phi )})</span>, <span>(Omega subset {mathbb {R}}^2)</span> is a bounded domain, and <i>f</i> has exponential critical growth. First, using reduction argument, truncation technique, Ekeland’s variational principle, and the Mountain Pass theorem, we obtain that the above system admits at least two solutions with different energy for <span>(lambda )</span> large enough and <span>(varepsilon )</span> fixed. Finally, we research the asymptotic behavior of solutions with respect to the parameters <span>(varepsilon )</span>.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A variational principle, fixed points and coupled fixed points on $$mathbb {P}$$ sets $$mathbb {P}$$ 集上的变分原理、定点和耦合定点
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-07-31 DOI: 10.1007/s11784-024-01123-w
Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov
{"title":"A variational principle, fixed points and coupled fixed points on $$mathbb {P}$$ sets","authors":"Valentin Georgiev, Atanas Ilchev, Boyan Zlatanov","doi":"10.1007/s11784-024-01123-w","DOIUrl":"https://doi.org/10.1007/s11784-024-01123-w","url":null,"abstract":"<p>We prove a generalization of Ekeland’s variational principal using the notion of <span>(mathbb {P})</span> sets. Using this result, we give proofs for fixed point theorems on partially ordered sets. Furthermore, one can obtain theorems for coupled fixed points using this technique. We demonstrate the procedure for proving such theorems.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Non-negative solutions of a sublinear elliptic problem 亚线性椭圆问题的非负解法
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-07-23 DOI: 10.1007/s11784-024-01120-z
Julián López-Gómez, Paul H. Rabinowitz, Fabio Zanolin
{"title":"Non-negative solutions of a sublinear elliptic problem","authors":"Julián López-Gómez, Paul H. Rabinowitz, Fabio Zanolin","doi":"10.1007/s11784-024-01120-z","DOIUrl":"https://doi.org/10.1007/s11784-024-01120-z","url":null,"abstract":"<p>In this paper, the existence of solutions, <span>((lambda ,u))</span>, of the problem </p><span>$$begin{aligned} left{ begin{array}{ll} -Delta u=lambda u -a(x)|u|^{p-1}u &amp;{} quad hbox {in }Omega , u=0 &amp;{}quad hbox {on};;partial Omega , end{array}right. end{aligned}$$</span><p>is explored for <span>(0&lt; p &lt; 1)</span>. When <span>(p&gt;1)</span>, it is known that there is an unbounded component of such solutions bifurcating from <span>((sigma _1, 0))</span>, where <span>(sigma _1)</span> is the smallest eigenvalue of <span>(-Delta )</span> in <span>(Omega )</span> under Dirichlet boundary conditions on <span>(partial Omega )</span>. These solutions have <span>(u in P)</span>, the interior of the positive cone. The continuation argument used when <span>(p&gt;1)</span> to keep <span>(u in P)</span> fails if <span>(0&lt; p &lt; 1)</span>. Nevertheless when <span>(0&lt; p &lt; 1)</span>, we are still able to show that there is a component of solutions bifurcating from <span>((sigma _1, infty ))</span>, unbounded outside of a neighborhood of <span>((sigma _1, infty ))</span>, and having <span>(u gneq 0)</span>. This non-negativity for <i>u</i> cannot be improved as is shown via a detailed analysis of the simplest autonomous one-dimensional version of the problem: its set of non-negative solutions possesses a countable set of components, each of them consisting of positive solutions with a fixed (arbitrary) number of bumps. Finally, the structure of these components is fully described.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141774169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
O’Neill’s theorem for PL approximations PL 近似值的奥尼尔定理
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-07-18 DOI: 10.1007/s11784-024-01117-8
Srihari Govindan, Lucas Pahl
{"title":"O’Neill’s theorem for PL approximations","authors":"Srihari Govindan, Lucas Pahl","doi":"10.1007/s11784-024-01117-8","DOIUrl":"https://doi.org/10.1007/s11784-024-01117-8","url":null,"abstract":"<p>We present a version of O’Neill’s theorem (Theorem 5.2 in O’Neill in Am J Math 75(3):497–509, 1953) for piecewise linear approximations.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744155","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Existence and asymptotic behavior of solutions for quasilinear Schrödinger equations involving p-Laplacian 涉及 p-Laplacian 的准线性薛定谔方程解的存在性和渐近行为
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-07-05 DOI: 10.1007/s11784-024-01118-7
Jiaxin Cao, Youjun Wang
{"title":"Existence and asymptotic behavior of solutions for quasilinear Schrödinger equations involving p-Laplacian","authors":"Jiaxin Cao, Youjun Wang","doi":"10.1007/s11784-024-01118-7","DOIUrl":"https://doi.org/10.1007/s11784-024-01118-7","url":null,"abstract":"<p>In this paper, we investigate the existence and asymptotic behavior of positive solutions for quasilinear Schrödinger equations involving <i>p</i>-Laplacian </p><span>$$begin{aligned} -Delta _{p}u + kappa Delta _{p}(u^2)u + (lambda A( x) + 1)|u|^{p-2}u = h(u), quad uin W^{1,p}(mathbb {R}^N), end{aligned}$$</span><p>where <span>(2&lt;p&lt;N)</span>, <span>(kappa ,)</span> <span>(lambda )</span> are parameters and <i>A</i>(<i>x</i>) is a potential. The problem is quite sensitive to the sign of <span>(kappa )</span> and there have been many results for <span>(kappa le 0.)</span> By means of minimization on the Nehari manifold together with perturbation type techniques, we establish the existence of positive solutions for small <span>(kappa &gt;0)</span> and large <span>(lambda )</span>. Moreover, we show that the solutions <span>(u_{kappa ,lambda })</span> converge in <span>(W^{1,p})</span> to a positive solution of <i>p</i>-Laplacian in a bounded domain as <span>((kappa ,lambda )rightarrow (0^+,+infty ))</span>. Our results extend some known results of <span>(kappa le 0)</span>.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141548169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the application of some fixed-point techniques to Fredholm integral equations of the second kind 关于一些定点技术在弗雷德霍姆第二类积分方程中的应用
IF 1.8 3区 数学
Journal of Fixed Point Theory and Applications Pub Date : 2024-06-28 DOI: 10.1007/s11784-024-01119-6
J. A. Ezquerro, M. A. Hernández-Verón
{"title":"On the application of some fixed-point techniques to Fredholm integral equations of the second kind","authors":"J. A. Ezquerro, M. A. Hernández-Verón","doi":"10.1007/s11784-024-01119-6","DOIUrl":"https://doi.org/10.1007/s11784-024-01119-6","url":null,"abstract":"<p>It is known that the global convergence of the method of successive approximations is obtained by means of the Banach contraction principle. In this paper, we study the global convergence of the method by means of a technique that uses auxiliary points and, as a consequence of this study, we obtain fixed-point type results on closed balls. We apply the study to nonlinear Fredholm integral equations of the second kind.</p>","PeriodicalId":54835,"journal":{"name":"Journal of Fixed Point Theory and Applications","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2024-06-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141502651","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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