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arXiv · 1603.01193

Infinite many Blow-up solutions for a Schr\"odinger quasilinear elliptic problem with a non-square diffusion term

Carlos Alberto Santos·Jiazheng Zhou
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Abstract

In this paper, we consider existence of positive solutions for the Schr\"odinger quasilinear elliptic problem $$ \left\{ \begin{array}{l} \Delta_pu+\Delta_p(|u|^{2\gamma})|u|^{2\gamma-2}u = a(x)g(u)~ \mbox{on}~ \mathbb{R}^N,\\ u>0\ \mbox{in}~\mathbb{R}^N,\ u(x)\stackrel{\left|x\right|\rightarrow \infty}{\longrightarrow} \infty, \end{array} \right. $$ where $a(x), ~x\in \mathbb{R}^N$ and $g(s)~s>0$ are a nonnegative and continuous functions with $g$ being nonincreasing as well, $\gamma>{1}/{2}$, and $N \geq 1$. By a dual approach we establish sufficient conditions for existence and multiplicity of solutions for this problem.

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Carlos Alberto Santos, Jiazheng Zhou. 2016-03-03. Infinite many Blow-up solutions for a Schr\"odinger quasilinear elliptic problem with a non-square diffusion term. https://arxiv.org/abs/1603.01193

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