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In this paper, we consider nonlinear Dirichlet problem driven by the p-Laplacian differential operator. Using variational methods based on the critical point theory and truncation techniques, we prove the existence of at least three nontrivial smooth solutions. The hypotheses on the nonlinearity incorporate in our framework of analysis both coercive and noncoercive problems. For the semilinear problem (p = 2), using Morse theory, we show the existence of four nontrivial smooth solutions.

Multiplicity of Solutions For p-Laplacian Equations Which Need Not be Coercive