Multiplicity of solutions for a class of nonhomogeneous quasilinear elliptic system with locally symmetric condition in $\mathbb{R}^N$

Cuiling Liu; Xingyong Zhang; Liben Wang

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arXiv · 2308.06128

Multiplicity of solutions for a class of nonhomogeneous quasilinear elliptic system with locally symmetric condition in $\mathbb{R}^N$

Cuiling Liu·Xingyong Zhang·Liben Wang

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Abstract

This paper is concerned with a class of nonhomogeneous quasilinear elliptic system driven by the locally symmetric potential and the small continuous perturbations in the whole-space $\mathbb{R}^N$. By a variant of Clark's theorem without the global symmetric condition and a Moser's iteration technique, we obtain the existence of multiple solutions when the nonlinear term satisfies some growth conditions only in a circle with center 0 and the perturbation term is any continuous function with a small parameter and no any growth hypothesis.

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Cuiling Liu, Xingyong Zhang, Liben Wang. 2023-08-11. Multiplicity of solutions for a class of nonhomogeneous quasilinear elliptic system with locally symmetric condition in $\mathbb{R}^N$. https://arxiv.org/abs/2308.06128

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