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arXiv · 1603.07158

On the existence of positive solutions for a quasilinear Schr\"{o}dinger equation

Haidong Liu·Leiga Zhao
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Abstract

This paper is concerned with the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u- \Delta(u^2)u =h(u), \ \ \mbox{in} \ \mathbb{R}^N, \end{equation*} where $N\geq 3$. Under appropriate assumptions on $V$ and $h$, we establish the existence of positive solutions. The main novelty is that, unlike most other papers on this problem, we do not assume $h$ is 4-superlinear at infinity.

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Haidong Liu, Leiga Zhao. 2016-03-23. On the existence of positive solutions for a quasilinear Schr\"{o}dinger equation. https://arxiv.org/abs/1603.07158

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