arXiv subjects

Zhangyi Yu

Publications and source records attributed to Zhangyi Yu.

3 recordsLinked to original sources

arXiv2025

Least energy solutions of two asymptotically cubic Kirchhoff equations on locally finite graphs

We study the existence of least energy solutions for two Kirchhoff equations with the asymptotically cubic nonlinearity $f(u)=\lambda u+\eta|u|^2u$ on a locally weighted and connected finite graph $G=(V,E)$. Such nonlinearity satisfies neither $\frac{F(u)}{u^4}\to +\infty$ as $|u|\to\infty$, where $F(u)=\int_0^uf(s)ds$, nor $\frac{f(u)}{u}\to 0$ as $u\to 0$. By utilizing the constrained variational method, we prove that there exist $\lambda_1\ge 0$ and $\eta_0\ge 0$ ($\lambda_1^*\ge 0$ and $\eta_0^*\ge 0$) such that these two equations have at least a least energy solution if $|\lambda| \eta_0$ ($\eta>\eta_0^*$).

math.AP↗

arXiv2024

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 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.

math.AP↗

arXiv2024

Infinitely many solutions for two generalized poly-Laplacian systems on weighted graphs

We investigate the multiplicity of solutions for a generalized poly-Laplacian system on weighted finite graphs and a generalized poly-Laplacian system with Dirichlet boundary value on weighted locally finite graphs, respectively, via the variational methods which are based on mountain pass theorem and topological degree theory. We obtain that these two systems have a sequence of minimax type solutions $\{(u_n,v_n)\}$ satisfying the energy functional $\varphi(u_n,v_n)\to +\infty$ as $n\to +\infty$ and a sequence of local minimum type solutions $\{(u_m^*,v_m^*)\}$ satisfying the energy functional $\varphi(u_m^*,v_m^*)\to -\infty$ as $m\to +\infty$.

math.AP↗