Parametric Robin double phase problems with critical growth on the boundary
Giuseppina D’Aguì, Angela Sciammetta, Elisabetta Tornatore, Patrick Winkert, Technische Universität Berlin, Institut für Mathematik, Straße des 17. Juni 136, 10623 Berlin, Germany
Abstract
<p style='text-indent:20px;'>The aim of this paper is to study a double phase problem with nonlinear boundary condition of critical growth and with a superlinear right-hand side that does not satisfy the Ambrosetti-Rabinowitz condition. Based on an equivalent norm in the Musielak-Orlicz Sobolev space along with variational tools and critical point theory, we prove the existence of at least two nontrivial, bounded weak solutions.
Topics & Concepts
Sobolev spaceMathematicsBounded functionNorm (philosophy)Critical point (mathematics)Parametric statisticsRobin boundary conditionNonlinear systemBoundary (topology)Mathematical analysisPure mathematicsFree boundary problemPhysicsStatisticsLawPolitical scienceQuantum mechanicsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringAnalytic and geometric function theory