### Multiplicity of multi-bump type nodal solutions for a class of elliptic problems in ${\Bbb R}^N$

DOI: http://dx.doi.org/10.12775/TMNA.2009.040

#### Abstract

In this paper, we establish existence and multiplicity of multi-bump

type nodal solutions for the following class of problems

$$

-\Delta u + (\lambda V(x)+ 1)u= f(u), \quad u> 0 \quad

\text{in } {\mathbb R}^N,

$$

where $N \geq 1$, $\lambda \in (0, \infty), f$ is a continuous function with

subcritical growth and $V\colon {\mathbb R}^N \rightarrow

{\mathbb R} $ is

a continuous function verifying some hypotheses.

type nodal solutions for the following class of problems

$$

-\Delta u + (\lambda V(x)+ 1)u= f(u), \quad u> 0 \quad

\text{in } {\mathbb R}^N,

$$

where $N \geq 1$, $\lambda \in (0, \infty), f$ is a continuous function with

subcritical growth and $V\colon {\mathbb R}^N \rightarrow

{\mathbb R} $ is

a continuous function verifying some hypotheses.

#### Keywords

Variational methods; nodal solutions; elliptic problems

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