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Multiple solutions for (p, 2)-equations at resonance

  • * Corresponding author: Nikolaos Papageorgiou

    * Corresponding author: Nikolaos Papageorgiou 
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  • We consider a nonlinear nonhomogeneous Dirichlet problem driven by the sum of a $p$-Laplacian and a Laplacian and a reaction term which is $(p-1)$-linear near $\pm \infty$ and resonant with respect to any nonprincipal variational eigenvalue of $(-\Delta_p,W^{1,p}_0(\Omega))$. Using variational tools together with truncation and comparison techniques and Morse Theory (critical groups), we establish the existence of six nontrivial smooth solutions. For five of them we provide sign information and order them.

    Mathematics Subject Classification: Primary: 35J20, 35J60; Secondary: 58E05.


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