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arXiv · 2408.02041

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

Zhangyi Yu·Junping Xie·Xingyong Zhang
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Abstract

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.

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Zhangyi Yu, Junping Xie, Xingyong Zhang. 2024-08-04. Nontrivial solutions for a $(p,q)$-Kirchhoff type system with concave-convex nonlinearities on locally finite graphs. https://doi.org/10.1186/s13661-024-01947-y

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