On noncoercive periodic systems with vector $p$-Laplacian

Petru Jebelean, Nikolaos S. Papageorgiou

Abstract


We consider nonlinear periodic systems driven by the vector
$p$-Laplacian. An existence and a multiplicity theorem are proved. In the
existence theorem the potential function is $p$-superlinear, but in general
does not satisfy the AR-condition. In the multiplicity theorem the
problem is strongly resonant with respect to the principal eigenvalue
$\lambda_0=0$. In both of the cases the Euler-Lagrange functional is
noncoercive and the method is variational.

Keywords


Vector p-Laplacian; p-superlinear potential; local linking; second deformation theorem; PS and C conditions

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