Communications in Mathematical Analysis

Multiplicity of Nodal Solutions for a Class of $p$-Laplacian Equations in $\mathbb{R}^{N}$

Y. H. Chen

Abstract

We consider a class of $p$-Laplacian equations in $\mathbb{R}^{N}$. By carefully analyzing the compactness of the Palais-Smale sequences and constructing Nehari manifolds, we prove that for every positive integer $m\geq 2$, there exists a nodal solution with at least $2m$ nodal domains.

Article information

Source
Commun. Math. Anal., Volume 12, Number 2 (2012), 120-136.

Dates
First available in Project Euclid: 16 March 2012

https://projecteuclid.org/euclid.cma/1331929875

Mathematical Reviews number (MathSciNet)
MR2905135

Zentralblatt MATH identifier
1266.35013

Subjects
Primary: 35J05
Secondary: , 35J20 35J60: Nonlinear elliptic equations

Citation

Chen, Y. H. Multiplicity of Nodal Solutions for a Class of $p$-Laplacian Equations in $\mathbb{R}^{N}$. Commun. Math. Anal. 12 (2012), no. 2, 120--136. https://projecteuclid.org/euclid.cma/1331929875