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- Title
Ground state solutions for a class of generalized quasilinear Schrödinger‐Maxwell system with critical growth.
- Authors
Zhang, Shulin; Liu, Wenbin
- Abstract
In this paper, we consider the following generalized quasilinear Schrödinger‐Maxwell system −div(g2(u)∇u)+g(u)g′(u)|∇u|2+V(x)u+ϕG(u)g(u)=h(x,u),x∈ℝ3,−Δϕ=G2(u),x∈ℝ3.$$ \left\{\begin{array}{ll}-\operatorname{div}\left({g}^2(u)\nabla u\right)+g(u){g}^{\prime }(u){\left|\nabla u\right|}^2+V(x)u+\phi G(u)g(u)=h\left(x,u\right),& x\in {\mathrm{\mathbb{R}}}^3,\\ {}-\Delta \phi ={G}^2(u),& x\in {\mathrm{\mathbb{R}}}^3.\end{array}\right. $$ Under suitable conditions on V$$ V $$, g$$ g $$, and h$$ h $$, we obtain the existence of ground state solutions with critical growth. To some extent, our results improve and supplement some existing relevant results.
- Publication
Mathematical Methods in the Applied Sciences, 2023, Vol 46, Issue 18, p19135
- ISSN
0170-4214
- Publication type
Article
- DOI
10.1002/mma.9615