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The Nehari Manifold for a p-Laplacian equation with concave-convex nonlinearities and sign-changing potential 具有凹凸非线性和变号势的p- laplace方程的Nehari流形
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/DEA-2019-11-16
Hong-Ying Li
{"title":"The Nehari Manifold for a p-Laplacian equation with concave-convex nonlinearities and sign-changing potential","authors":"Hong-Ying Li","doi":"10.7153/DEA-2019-11-16","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-16","url":null,"abstract":". In this paper, we study the multiplicity of solutions for a class of concave-convex p - Laplacian equations with the combined effect of coef fi cient functions of concave-convex terms. By the Nehari method and some analysis techniques, we obtain an exact constant for the effect of coef fi cient functions of concave-convex terms to ensure this problem has two nonzero and nonnegative solutions and give the relation of size of the two solutions. Moreover, under some stronger conditions, we prove that the two solutions are positive. Our results generalize and improve some known results in the literature.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Positive solutions for a singular coupled system of nonlinear higher-order fractional q-difference boundary value problems with two parameters 一类具有两个参数的非线性高阶分数阶q差分边值问题的奇异耦合系统的正解
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/dea-2019-11-25
Wengui Yang
{"title":"Positive solutions for a singular coupled system of nonlinear higher-order fractional q-difference boundary value problems with two parameters","authors":"Wengui Yang","doi":"10.7153/dea-2019-11-25","DOIUrl":"https://doi.org/10.7153/dea-2019-11-25","url":null,"abstract":"In this paper, we are concern with the existence of positive solutions for a singular system of nonlinear fractional q -difference equations with coupled integral boundary conditions and two parameters. By using the properties of the Green’s function and Guo-Krasnosel’skii fixed point theorem, some existence results of at least one positive solution are obtained. As applications, two examples are presented to illustrate the main results. Mathematics subject classification (2010): 39A13, 34B18, 34A08.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130441","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Positive solutions to a nonlinear sixth order boundary value problem 一类非线性六阶边值问题的正解
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/DEA-2019-11-13
Bo Yang
{"title":"Positive solutions to a nonlinear sixth order boundary value problem","authors":"Bo Yang","doi":"10.7153/DEA-2019-11-13","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-13","url":null,"abstract":"We consider a sixth order two point boundary value problem. Upper and lower estimates for positive solutions of the problem are proved. Sufficient conditions for the existence and nonexistence of positive solutions for the problem are obtained. An example is included to illustrate the results.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"38 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130121","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Positive solutions for fractional integro-boundary value problem of order (1,2) on an unbounded domain 无界域上(1,2)阶分数阶积分边值问题的正解
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/DEA-2019-11-14
V. Gupta, J. Dabas
{"title":"Positive solutions for fractional integro-boundary value problem of order (1,2) on an unbounded domain","authors":"V. Gupta, J. Dabas","doi":"10.7153/DEA-2019-11-14","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-14","url":null,"abstract":". In this manuscript, we study a system of fractional integro boundary value problem on unbounded domain. The solution of the system is de fi ned in terms of the Green’s function. We have established the existence and uniqueness results by utilizing the fi xed point theorems. The main outcomes and assumptions are veri fi ed via some examples.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Final state problem for the nonlocal nonlinear Schrödinger equation with dissipative nonlinearity 具有耗散非线性的非局部非线性Schrödinger方程的终态问题
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/dea-2019-11-23
Mamoru Okamoto, Kota Uriya
{"title":"Final state problem for the nonlocal nonlinear Schrödinger equation with dissipative nonlinearity","authors":"Mamoru Okamoto, Kota Uriya","doi":"10.7153/dea-2019-11-23","DOIUrl":"https://doi.org/10.7153/dea-2019-11-23","url":null,"abstract":". Weconsider the asymptotic behavior of solutions to the nonlocal nonlinear Schr¨odinger equation with dissipative nonlinearity. We prove that there exists a solution which has different behavior from that of the typical cubic nonlinear Schr¨odinger equation.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Second order two-parametric quantum boundary value problems 二阶双参数量子边值问题
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/dea-2019-11-10
Yousef Gholami
{"title":"Second order two-parametric quantum boundary value problems","authors":"Yousef Gholami","doi":"10.7153/dea-2019-11-10","DOIUrl":"https://doi.org/10.7153/dea-2019-11-10","url":null,"abstract":"In this paper we study second order two-parametric quantum boundary value problems. The main aims of this paper are presented in two steps. In the first step, we consider second order two-parametric quantum boundary value problems with general nonlinearities and by the use of Krasnoselskii fixed point theorem on positive cones we provide some sufficient conditions to reach the existence, multiplicity and nonexistence of positive solutions. At the and of this step, some illustrative examples are given to show practical implementability of the obtained theoretical results. In the second step, we consider the corresponding two-parametric quantum eigenvalue problems and in the light of Lyapunov inequalities, we present a lower bound estimation for positive eigenvalues. We complete this step with a numerical evaluation to identify validity of the obtained lower bound.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"158 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130054","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Progressive contractions, measures of non-compactness and quadratic integral equations 渐进收缩，非紧性的度量和二次积分方程
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/dea-2019-11-12
T. Burton, I. Purnaras
{"title":"Progressive contractions, measures of non-compactness and quadratic integral equations","authors":"T. Burton, I. Purnaras","doi":"10.7153/dea-2019-11-12","DOIUrl":"https://doi.org/10.7153/dea-2019-11-12","url":null,"abstract":"Classical fixed point theorems often begin with the assumption that we have a mapping P of a non-empty, closed, bounded, convex set G in a Banach space into itself. Then a number of conditions are added which will ensure that there is at least one fixed point in the set G . These fixed point theorems have been very effective with many problems in applied mathematics, particularly for integral equations containing a term ∫ t 0 A(t− s)v(t,s,x(s))ds, because such terms frequently map sets of bounded continuous functions into compact sets. But there is a large and important class of integral equations from applied mathematics containing such a term with a coefficient function f (t,x) which destroys all compactness. Investigators have then turned to Darbo’s fixed point theorem and measures of non-compactness to get a (possibly non-unique) fixed point. In this paper: a) We offer an elementary alternative to measures of non-compactness and Darbo’s theorem by using progressive contractions. This method yields a unique fixed point (unlike Darbo’s theorem) which, in turn, by default yields asymptotic stability as introduced in [1]. b) We lift the growth requirements in both x and t seen using Darbo’s theorem. c) We offer a technique for finding the mapping set G .","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
A non Green's function approach to fractional Lyapunov-type inequalities with applications to multivariate domains 分数阶lyapunov型不等式的非格林函数方法及其在多元域上的应用
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/DEA-2019-11-19
Sougata Dhar, J. Kelly
{"title":"A non Green's function approach to fractional Lyapunov-type inequalities with applications to multivariate domains","authors":"Sougata Dhar, J. Kelly","doi":"10.7153/DEA-2019-11-19","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-19","url":null,"abstract":". We derive Lyapunov-type inequalities for certain fractional differential equations of order α , where 1 < α (cid:2) 2 or 2 < α (cid:2) 3. The methods used within rely on considering the maximum value of a nontrivial solution in a given interval as opposed to traditional methods which utilize the Green’s function. This particular method provides versatility and can be applied to other fractional boundary value problems where the Green’s function is inaccessible. Furthermore, we demonstrate how the inequalities may be extended to fractional multivariate equations in both the left and right-fractional cases.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"4 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects 具有非线性边界条件的四阶方程的多重解:理论和数值方面
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/DEA-2019-11-15
C. Martinez, A. Martinez, G. Bressan, E. V. Castelani, Roberto Molina de Souza
{"title":"Multiple solutions for a fourth order equation with nonlinear boundary conditions: theoretical and numerical aspects","authors":"C. Martinez, A. Martinez, G. Bressan, E. V. Castelani, Roberto Molina de Souza","doi":"10.7153/DEA-2019-11-15","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-15","url":null,"abstract":". We consider in this work the fourth order equation with nonlinear boundary condi- tions. We present the result for the existence of multiple solutions based on the Avery-Peterson fi xed-point theorem. This work is also a study for numerical solutions based on the Levenberg- Maquardt method with a heuristic strategy for initial points that proposes to numerically deter-mine multiple solutions to the problem addressed.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Hölder continuity up to the boundary of solutions to nonlinear fourth-order elliptic equations with natural growth terms Hölder具有自然生长项的非线性四阶椭圆方程解的边界连续性
IF 0.3
Differential Equations & Applications Pub Date : 2019-01-01 DOI: 10.7153/DEA-2019-11-03
S. Bonafede, M. Voitovych
{"title":"Hölder continuity up to the boundary of solutions to nonlinear fourth-order elliptic equations with natural growth terms","authors":"S. Bonafede, M. Voitovych","doi":"10.7153/DEA-2019-11-03","DOIUrl":"https://doi.org/10.7153/DEA-2019-11-03","url":null,"abstract":"In a bounded open set Ω ⊂ Rn , n 3 , we consider the nonlinear fourth-order partial differential equation ∑|α|=1,2 (−1)|α|Dα Aα(x,u,Du,Du)+B(x,u,Du,Du) = 0. It is assumed that the principal coefficients {Aα}|α|=1,2 satisfy the growth and coercivity conditions suitable for the energy space W̊ 1,q 2,p (Ω) = W̊ 1,q(Ω)∩W̊ 2,p(Ω) , 1 < p< n/2 , 2p < q < n . The lower-order term B(x,u,Du,D2u) behaves as b(u) {|Du|q + |D2u|p}+g(x) where g ∈ Lτ (Ω) , τ > n/q . We establish the Hölder continuity up to the boundary of any solution u∈ W̊ 1,q 2,p (Ω)∩L∞(Ω) by using the measure density condition on ∂Ω , an interior local result and a modified Moser method with special test function.","PeriodicalId":51863,"journal":{"name":"Differential Equations & Applications","volume":"1 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"71130405","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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