Rocky Mountain Journal of Mathematics

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

Lin Zhao and Peihao Zhao

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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.

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

First available in Project Euclid: 31 October 2014

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Zentralblatt MATH identifier

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

Critical point theory variational methods three solutions Moser iteration


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.

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