Nontrivial solutions for a \((p,q)\)-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs

By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a \((p,q)\)-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finit...

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Bibliographic Details
Published inarXiv.org
Main Authors Yu, Zhangyi, Xie, Junping, Zhang, Xingyong
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 04.08.2024
Subjects
Boundary conditions
Mathematics - Analysis of PDEs
Perturbation
Theorems
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Summary:By using the well-known mountain pass theorem and Ekeland's variational principle, we prove that there exist at least two fully-non-trivial solutions for a \((p,q)\)-Kirchhoff elliptic system with the Dirichlet boundary conditions and perturbation terms on a locally weighted and connected finite graph \(G=(V,E)\).We also present a necessary condition of the existence of semi-trivial solutions for the system. Moreover, by using Ekeland's variational principle and Clark's Theorem, respectively, we prove that the system has at least one or multiple semi-trivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions.
ISSN:2331-8422
DOI:10.48550/arxiv.2408.02041