Existence results for double phase problems depending on Robin and Steklov eigenvalues for the <i>p</i> -Laplacian
Said El Manouni, Greta Marino, Patrick Winkert
Abstract
Abstract In this paper we study double phase problems with nonlinear boundary condition and gradient dependence. Under quite general assumptions we prove existence results for such problems where the perturbations satisfy a suitable behavior in the origin and at infinity. Our proofs make use of variational tools, truncation techniques and comparison methods. The obtained solutions depend on the first eigenvalues of the Robin and Steklov eigenvalue problems for the p -Laplacian.
Topics & Concepts
Eigenvalues and eigenvectorsMathematicsTruncation (statistics)Mathematical proofNonlinear systemLaplace operatorBoundary (topology)Applied mathematicsMathematical analysisInfinityRobin boundary conditionPhase (matter)Pure mathematicsGeometryPhysicsNeumann boundary conditionQuantum mechanicsStatisticsAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsAdvanced Numerical Methods in Computational Mathematics