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A nonlinear eigenvalue problem for the periodic scalar $p$-Laplacian

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  • We study a parametric nonlinear periodic problem driven by the scalar $p$-Laplacian. We show that if $\hat \lambda_1 >0$ is the first eigenvalue of the periodic scalar $p$-Laplacian and $\lambda> \hat \lambda_1$, then the problem has at least three nontrivial solutions one positive, one negative and the third nodal. Our approach is variational together with suitable truncation, perturbation and comparison techniques.
    Mathematics Subject Classification: Primary: 34B15, 34B18; Secondary: 34C25.

    Citation:

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