### On noncoercive periodic systems with vector $p$-Laplacian

#### 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.

$p$-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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