6533b838fe1ef96bd12a3d87
RESEARCH PRODUCT
A nonlinear eigenvalue problem for the periodic scalar p-Laplacian
Giuseppina BarlettaRoberto LivreaNikolaos S. Papageorgiousubject
PhysicsApplied MathematicsScalar (mathematics)AnalysiGeneral MedicineMathematics::Spectral TheoryLambdaSecond deformation theoremParametric equationNonlinear systemp-LaplacianConstant sign and nodal solutionExtremal solutionDivide-and-conquer eigenvalue algorithmParametric equationAnalysisEigenvalues and eigenvectorsParametric statisticsMathematical physicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2014-01-01 |