Constant sign and nodal solutions for superlinear ( <i>p</i> , <i>q</i> )–equations with indefinite potential and a concave boundary term
Nikolaos S. Papageorgiou, Youpei Zhang
Abstract
Abstract We consider a nonlinear elliptic equation driven by the ( p , q )–Laplacian plus an indefinite potential. The reaction is ( p − 1)–superlinear and the boundary term is parametric and concave. Using variational tools from the critical point theory together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information and which are linearly ordered.
Topics & Concepts
MathematicsMathematical analysisBoundary value problemNonlinear systemTerm (time)Sign (mathematics)Critical point (mathematics)Mountain pass theoremParametric statisticsTruncation (statistics)Perturbation (astronomy)Elliptic curveLaplace operatorPhysicsQuantum mechanicsStatisticsNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringAdvanced Mathematical Physics Problems