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arXiv · 1304.5366

Multiple solutions for a quasilinear Schr\"{o}dinger equation on $\mathbb{R}^{N}$}

Claudianor O. Alves·Giovany M. Figueiredo
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Abstract

The multiplicity of positive weak solutions for a quasilinear Schr\"{o}dinger equations $-L_p u +(\lambda A(x)+1)|u|^{p-2}u= h(u)$ in $\mathbb{R}^N$ is established, where $L_p u\doteq \epsilon^{p}\Delta_p u +\epsilon^{p}\Delta_p (u^2)u$, $A$ is a nonnegative continuous function and nonlinear term $h$ has a subcritical growth. We achieved our results by using minimax methods and Lusternik-Schnirelman theory of critical points.

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Claudianor O. Alves, Giovany M. Figueiredo. 2013-04-19. Multiple solutions for a quasilinear Schr\"{o}dinger equation on $\mathbb{R}^{N}$}. https://arxiv.org/abs/1304.5366

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