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arxiv: 1412.4219 · v1 · submitted 2014-12-13 · 🧮 math.AP

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Multiplicity of multi-bump type nodal solutions for a class of elliptic problems with exponential critical growth in mathbb{R}²

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keywords mathbbclasscontinuouscriticalexponentialfunctiongrowthlambda
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In this paper, we establish the existence and multiplicity of multi-bump nodal solutions for the following class of problems $$ -\Delta u+(\lambda V(x)+1)u=f(u),~~\mbox{in}~~\mathbb{R}^2, $$ where $\lambda\in(0,\infty)$, $f$ is a continuous function with exponential critical growth and $V:\mathbb{R}^2\to \mathbb{R}$ is a continuous function verifying some hypotheses.

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