Existence and multiplicity of solutions for a class of $(p,q)$-Kirchhoff system with combined nonlinearities on graphs
Year: 2024
Type: article
Abstract: By using the well-known mountain-pass theorem and Ekeland’s variational principle, we prove that there exist at least two fully nontrivial 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 semitrivial 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 semitrivial solutions when the perturbation terms satisfy different assumptions. Finally, we present a nonexistence result of solutions.
Source: Boundary Value Problems
Authors: Zhangyi Yu, Junping Xie, Xingyong Zhang
Institution: Kunming University of Science and Technology
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,790
OpenAlex ID: W4403489397