Rocky Mountain Journal of Mathematics

The existence of three solutions for $p$-Laplacian problems with critical and supercritical growth

Lin Zhao and Peihao Zhao

Full-text: Open access

Abstract

In this paper we deal with the existence and multiplicity of solutions for the $p$-Laplacian problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we extend the result obtained by Ricceri \cite{14} to the critical and supercritical case.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 4 (2014), 1383-1397.

Dates
First available in Project Euclid: 31 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1414760960

Digital Object Identifier
doi:10.1216/RMJ-2014-44-4-1383

Mathematical Reviews number (MathSciNet)
MR3274355

Zentralblatt MATH identifier
1350.35083

Subjects
Primary: 35J20: Variational methods for second-order elliptic equations 35J60: Nonlinear elliptic equations 35J92: Quasilinear elliptic equations with p-Laplacian

Keywords
Critical point theory variational methods three solutions Moser iteration

Citation

Zhao, Lin; Zhao, Peihao. The existence of three solutions for $p$-Laplacian problems with critical and supercritical growth. Rocky Mountain J. Math. 44 (2014), no. 4, 1383--1397. doi:10.1216/RMJ-2014-44-4-1383. https://projecteuclid.org/euclid.rmjm/1414760960


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