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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 [14] to the critical and supercritical case.

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