Multiple solutions for nonhomogeneous generalized quasilinear Kirchhoff-Schrödinger-Poisson system
Year: 2026
Type: article
Abstract: In this paper, we consider a class of modified Schrödinger-Poisson system with Kirchhoff-type perturbation by use of variational methods: 0.1$$ \left \{ \textstyle\begin{array}{l@{\quad}l} \bigg(1+b\int _{\mathbb{R}^{3}}g^{2}(u)|\nabla u|^{2}dx\bigg)[- \textrm{div}(g^{2}(u)\nabla u)+g(u)g'(u)|\nabla u|^{2}] \\ + V(x)u + \phi u=h(u)+{\vartheta (x)},&x\in \mathbb{R}^{3}, \\ -\Delta \phi =u^{2},&x\in \mathbb{R}^{3}, \end{array}\displaystyle \right . $$ where $b\geq 0$, $g\in C^{1}(\mathbb{R},\,\mathbb{R}^{+})$, V and h are continuous functions, $\vartheta \not \equiv 0$. There are three major ingredients in two cases. Firstly, for $\vartheta =0$, we demonstrated the system (0.1) has a nontrivial ground state solution for $h(u)=\lambda f(u)+g(u)G^{5}(u)$, where $G(u)=\int _{0}^{u}g(t)dt$. Moreover, when nonlinear term $h(u)$ satisfies appropriate assumptions, a sequence of weak solutions were obtained by Clark’s theorem. Finally, for $\vartheta \neq 0$, with the help of Jeanjean theorem and cut-off function, at least two positive solutions of (0.1) were gained. To the best of our knowledge, this paper is one of the first contribution to study the nonhomogeneous generalized Kirchhoff-Schrödinger-Poisson system.
Authors: Yaru Wang, Jing Zhang
Institution: Inner Mongolia Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $1,890
OpenAlex ID: W7131651809