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Lyapunov-type inequalities for third order nonlinear equations 三阶非线性方程的lyapunov型不等式
Differential Equations & Applications Pub Date : 2022-04-15 DOI: 10.7153/dea-2022-14-18
Brian C. Behrens, Sougata Dhar
{"title":"Lyapunov-type inequalities for third order nonlinear equations","authors":"Brian C. Behrens, Sougata Dhar","doi":"10.7153/dea-2022-14-18","DOIUrl":"https://doi.org/10.7153/dea-2022-14-18","url":null,"abstract":". We derive Lyapunov-type inequalities for general third order nonlinear equations in- volving multiple ψ -Laplacian operators of the form where ψ 2 and ψ 1 are odd, increasing functions, ψ 2 is super-multiplicative, ψ 1 is sub-multiplicative, and 1 ψ 1 is convex, and f is a continuous function which satisfies a sign condition. Our results utilize q + and q − , as opposed to | q | which appears in most results in the literature. Addi- tionally, these new inequalities generalize previously obtained results, and the proofs utilize a different technique than most other works in the literature. Furthermore, using the obtained in- equalities, we obtain a constraint on the location of the maximum of a solution, properties of oscillatory solutions, and an upper bound for the number of zeroes.","PeriodicalId":179999,"journal":{"name":"Differential Equations & Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131621400","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
Stability of solutions to abstract evolution equations in Banach spaces under nonclassical assumptions 非经典假设下Banach空间抽象演化方程解的稳定性
Differential Equations & Applications Pub Date : 2021-03-29 DOI: 10.7153/dea-2022-14-37
N. S. Hoang
{"title":"Stability of solutions to abstract evolution equations in Banach spaces under nonclassical assumptions","authors":"N. S. Hoang","doi":"10.7153/dea-2022-14-37","DOIUrl":"https://doi.org/10.7153/dea-2022-14-37","url":null,"abstract":"The stability of the solution to the equation (∗)u̇ = F (t, u) + f(t), t ≥ 0, u(0) = u0 is studied. Here F (t, u) is a nonlinear operator in a Banach space X for any fixed t ≥ 0 and F (t, 0) = 0, ∀t ≥ 0. We assume that the Fréchet derivative of F (t, u) is Hölder continuous of order q > 0 with respect to u for any fixed t ≥ 0, i.e., ‖F ′ u(t, w) − F ′ u(t, v)‖ ≤ α(t)‖v − w‖ , q > 0. We proved that the equilibrium solution v = 0 to the equation v̇ = F (t, v) is Lyapunov stable under persistently acting perturbation f(t) if supt≥0 ∫ t 0 α(ξ)‖U(t, ξ)‖ dξ < ∞ and supt≥0 ‖U(t)‖ < ∞. Here, U(t) := U(t, 0) and U(t, ξ) is the solution to the equation d dt U(t, ξ) = F ′ u(t, 0)U(t, ξ), t ≥ ξ, U(ξ, ξ) = I, where I is the identity operator in X . Sufficient conditions for the solution u(t) to equation (*) to be bounded and for limt→∞ u(t) = 0 are proposed and justified. Stability of solutions to equations with unbounded operators in Hilbert spaces is also studied.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124988830","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
Bifurcations of limit cycles in piecewise smooth Hamiltonian system with boundary perturbation 具有边界摄动的分段光滑哈密顿系统极限环的分岔
Differential Equations &amp; Applications Pub Date : 2019-12-20 DOI: 10.7153/dea-2022-14-34
Nanasaheb Phatangare, Krishnat D. Masalkar, S. Kendre
{"title":"Bifurcations of limit cycles in piecewise smooth Hamiltonian system with boundary perturbation","authors":"Nanasaheb Phatangare, Krishnat D. Masalkar, S. Kendre","doi":"10.7153/dea-2022-14-34","DOIUrl":"https://doi.org/10.7153/dea-2022-14-34","url":null,"abstract":"In this paper, the general planar piecewise smooth Hamiltonian system with period annulus around the center at the origin is considered. We obtain the expressions for the first order and the second order Melnikov functions of it's general second order perturbation, which can be used to find the number of limit cycles bifurcated from periodic orbits. Further, we have shown that the number of limit cycles of the system $dot{X}=begin{cases} (H_y^+,-H_x^+) & mbox{if}~y>varepsilon f(x) (H_y^-,-H_x^-) & mbox{if}~y<varepsilon f(x) end{cases}$ equals to the number of positive zeros of $f$ when at $varepsilon=0$ the system has a period annulus around the origin.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127216638","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
Bounded and unbounded positive solutions for singular φ-Laplacians coupled system on the half-line with first-order derivative dependence 具有一阶导数依赖的半线上φ- laplace奇异耦合系统的有界和无界正解
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2023-15-10
Kamal Bachouche, Dhehbiya Belal, Abdelhamid Benmezaï
{"title":"Bounded and unbounded positive solutions for singular φ-Laplacians coupled system on the half-line with first-order derivative dependence","authors":"Kamal Bachouche, Dhehbiya Belal, Abdelhamid Benmezaï","doi":"10.7153/dea-2023-15-10","DOIUrl":"https://doi.org/10.7153/dea-2023-15-10","url":null,"abstract":". In this paper we prove by means of expansion and compression of a cone principle, the existence of a positive solution to the second order boundary value problem","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115153216","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
Existence results for a system of boundary value problems for hybrid fractional differential equations 一类混合分数阶微分方程边值问题的存在性结果
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2022-14-19
Shaista Gul, R. Khan
{"title":"Existence results for a system of boundary value problems for hybrid fractional differential equations","authors":"Shaista Gul, R. Khan","doi":"10.7153/dea-2022-14-19","DOIUrl":"https://doi.org/10.7153/dea-2022-14-19","url":null,"abstract":". In this paper, we study a system of nonlinear boundary value problems (BVPs) con- sisting of more general class of sequential hybrid fractional equations (SHFDEs) together with a class of nonlinear boundary conditions at both end points of the domain. The nonlinear func- tions involved depend explicitly on the fractional derivatives. We study necessary conditions required for existence of solutions to the suggested system of BVPs under the Caratheodory con- ditions using the technique of measure of noncompactness and degree theory. We also develop conditions for uniqueness results and also on stability analysis.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116101965","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
Initial boundary value problem for a time fractional wave equation on a metric graph 度量图上时间分数阶波动方程的初边值问题
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2023-15-02
Z. Sobirov, O. Abdullaev, J. R. Khujakulov
{"title":"Initial boundary value problem for a time fractional wave equation on a metric graph","authors":"Z. Sobirov, O. Abdullaev, J. R. Khujakulov","doi":"10.7153/dea-2023-15-02","DOIUrl":"https://doi.org/10.7153/dea-2023-15-02","url":null,"abstract":". This work devoted to IBVP problem for a time-fractional differential equation on the regular metric tree graph. Using the method of separation of variables we fi nd exact solution of the investigated problem in the form of Fourier series. Special case for these problem are discussed, moreover in this case eigenvalues and corresponding eigenfunctions are found exactly. Suf fi cient classes of given functions, which provides an existence and uniqueness of solution of the considered problem, are de fi ned. Using a-priori estimates for the solution, uniqueness of solution is proved.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114447009","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
Green's function for a discrete fractional boundary value problem 离散分数边值问题的格林函数
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2022-14-10
J. Jonnalagadda, N. S. Gopal
{"title":"Green's function for a discrete fractional boundary value problem","authors":"J. Jonnalagadda, N. S. Gopal","doi":"10.7153/dea-2022-14-10","DOIUrl":"https://doi.org/10.7153/dea-2022-14-10","url":null,"abstract":". In this article, we deduce the expression and the main properties of the Green’s func- tion related to a general nabla fractional difference equation with constant coef fi cients coupled to Dirichlet conditions. In particular, we prove that such function has constant sign on their set of de fi nition, and also satis fi es some additional properties that are fundamental to de fi ne a suitable Banach space, where to ensure the existence and uniqueness of solutions of nonlinear problems.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121677897","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
P-periodic solutions of a q-integral equation with finite delay 有限时滞q积分方程的p周期解
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2022-14-23
Muhammad N. Islam, Jeffrey T. Neugebauer
{"title":"P-periodic solutions of a q-integral equation with finite delay","authors":"Muhammad N. Islam, Jeffrey T. Neugebauer","doi":"10.7153/dea-2022-14-23","DOIUrl":"https://doi.org/10.7153/dea-2022-14-23","url":null,"abstract":". A Volterra type integral equation with a fi nite delay is considered on a discrete non- additive time scale domain q N 0 = { q n : n ∈ N 0 } , where k ∈ N , q > 1. The existence of periodic solutions of this equation, which we call a q -integral equation, are shown employing the con- traction mapping principle and a fi xed point theorem due to Krasnosel’skii.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114859511","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
Existence results for the σ-Hilfer hybrid fractional boundary value problem involving a weighted φ-Laplacian operator 涉及加权φ- laplace算子的σ-Hilfer混合分数边值问题的存在性结果
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2022-14-05
Nadir Benkaci-Ali
{"title":"Existence results for the σ-Hilfer hybrid fractional boundary value problem involving a weighted φ-Laplacian operator","authors":"Nadir Benkaci-Ali","doi":"10.7153/dea-2022-14-05","DOIUrl":"https://doi.org/10.7153/dea-2022-14-05","url":null,"abstract":". In this paper, we are interested in the existence of positive solutions for the Hilfer hybrid fractional equation involving a weighted two dimensional φ -Laplacian operator with the integral-in fi nite point boundary conditions. In this approach, we transform the given fractional differential equation into an equivalent integral equation. Then we establish suf fi cient conditions and employ the fi xed point index arguments to obtain new results on the existence of positive solutions. Examples illustrating the main results are also constructed. This work contains several new ideas, and gives a uni fi ed approach applicable to many boundary value problems involving ( p , q ) -Laplacian type operators.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128936794","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
Convexity in fractional h-discrete calculus 分数阶h离散微积分中的凸性
Differential Equations &amp; Applications Pub Date : 1900-01-01 DOI: 10.7153/dea-2022-14-22
F. Atici, J. Jonnalagadda
{"title":"Convexity in fractional h-discrete calculus","authors":"F. Atici, J. Jonnalagadda","doi":"10.7153/dea-2022-14-22","DOIUrl":"https://doi.org/10.7153/dea-2022-14-22","url":null,"abstract":". In this paper, we consider a time scale h N a , where a ∈ R and h ∈ R + . The fractional h -difference operator is de fi ned in the sense of Riemann–Liouville with the forward difference operator Δ . First, we discuss monotonicity concept via fractional h -difference operators for the functions de fi ned on h N a . Second, we obtain some criteria to have the functions be ν -convex.","PeriodicalId":179999,"journal":{"name":"Differential Equations &amp; Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128244869","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
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