Topological Methods in Nonlinear Analysis

Multiplicity of nonradial solutions for a class of quasilinear equations on annulus with exponential critical growth

Claudianor O. Alves and Luciana R. de Freitas

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Abstract

In this paper, we establish the existence of many rotationally non-equivalent and nonradial solutions for the following class of quasilinear problems \begin{equation} \begin{cases} -\Delta_{N} u = \lambda f(|x|,u) &x\in \Omega_r,\\ u > 0 &x\in \Omega_r,\\ u=0 &x\in \partial\Omega_r, \end{cases} \tag{$\textrm{P}$} \end{equation} where $\Omega_r = \{ x \in \mathbb{R}^{N}: r < |x| < r+1\}$, $N \geq 2$, $N\neq 3$, $r > 0$, $\lambda > 0$, $\Delta_{N}u= {\rm div}(|\nabla u|^{N-2}\nabla u ) $ is the $N$-Laplacian operator and $f$ is a continuous function with exponential critical growth.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 39, Number 2 (2012), 243-262.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461243180

Mathematical Reviews number (MathSciNet)
MR2985880

Zentralblatt MATH identifier
1275.35111

Citation

Alves, Claudianor O.; de Freitas, Luciana R. Multiplicity of nonradial solutions for a class of quasilinear equations on annulus with exponential critical growth. Topol. Methods Nonlinear Anal. 39 (2012), no. 2, 243--262. https://projecteuclid.org/euclid.tmna/1461243180


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