Search results for "Second deformation theorem"

showing 2 items of 2 documents

Pairs of nontrivial smooth solutions for nonlinear Neumann problems

2020

Abstract We consider a nonlinear Neumann problem driven by a nonhomogeneous differential operator with a reaction term that exhibits strong resonance at infinity. Using variational tools based on the critical point theory, we prove the existence of two nontrivial smooth solutions.

Nonlinear systemStrong resonanceSettore MAT/05 - Analisi MatematicaApplied MathematicsC_c-conditionMathematical analysisNeumann boundary conditionDifferential operatorCritical point (mathematics)Second deformation theoremMathematicsNonlinear regularity
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A nonlinear eigenvalue problem for the periodic scalar p-Laplacian

2014

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.

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 physics
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