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arXiv · 2205.12298

Existence of positive solution for a class of quasilinear Schr\"odinger equations with potential vanishing at infinity on nonreflexive Orlicz-Sobolev spaces

L. da Silva·M. Souto
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Abstract

In this paper we investigate the existence of positive solution for a class of quasilinear problem on an Orlicz-Sobolev space that can be nonreflexive $$- \Delta_{\Phi} u +V(x)\phi(|u|)u= K(x)f(u)\mbox{ in } \mathbb{R}^{N}$$ where $N\geq2$, $V,K$ are nonnegative continuous functions and $f$ is a continuous function with a quasicritical growth. Here we extend the Hardy-type inequalities presented in \cite{AlvesandMarco} to nonreflexive Orlicz spaces. Through inequalities together with a variational method for non-differentiable functionals we will obtain a ground state solution. We analyze also the problem with $V=0$.

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L. da Silva, M. Souto. 2022-05-24. Existence of positive solution for a class of quasilinear Schr\"odinger equations with potential vanishing at infinity on nonreflexive Orlicz-Sobolev spaces. https://arxiv.org/abs/2205.12298

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