## Differential and Integral Equations

- Differential Integral Equations
- Volume 19, Number 2 (2006), 143-162.

### Existence and multiplicity of positive solutions to a $p$-Laplacian equation in $\Bbb R^N$

Claudianor O. Alves and Giovany M. Figueiredo

#### Abstract

In this work we study the existence, multiplicity and concentration of positive solutions for the following class of problem \begin{equation} - \epsilon^{p} \Delta_{p}u + V(z)|u|^{p-2}u=f(u), \,\,\, u(z) > 0, \forall \ z \in \mathbb R^N , \tag*{$(P_{\epsilon})$} \end{equation} where $\Delta_{p}u$ is the p-Laplacian operator, $\epsilon$ is a positive parameter, $2 \leq p < N, V:\mathbb R^N \to \mathbb R$ is a continuous functions and $f:\mathbb R \to \mathbb R$ is a function of $C^{1}$ class.

#### Article information

**Source**

Differential Integral Equations, Volume 19, Number 2 (2006), 143-162.

**Dates**

First available in Project Euclid: 21 December 2012

**Permanent link to this document**

https://projecteuclid.org/euclid.die/1356050522

**Mathematical Reviews number (MathSciNet)**

MR2194501

**Zentralblatt MATH identifier**

1212.35107

**Subjects**

Primary: 35J60: Nonlinear elliptic equations

Secondary: 35B25: Singular perturbations 47J30: Variational methods [See also 58Exx] 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

#### Citation

Alves, Claudianor O.; Figueiredo, Giovany M. Existence and multiplicity of positive solutions to a $p$-Laplacian equation in $\Bbb R^N$. Differential Integral Equations 19 (2006), no. 2, 143--162. https://projecteuclid.org/euclid.die/1356050522