On nontrivial solutions of nonlinear Schrödinger equations with sign-changing potential
Wei Chen, Yue Wu, Seong Tae Jhang
Abstract
Abstract In this paper, we consider the superlinear Schrödinger equation with bounded potential well. The potential here is allowed to be sign-changing. Without assuming the Ambrosetti–Rabinowitz-type condition, we prove the existence of a nontrivial solution and multiplicity results.
Topics & Concepts
MathematicsSign (mathematics)Bounded functionOrdinary differential equationPartial differential equationNonlinear systemMultiplicity (mathematics)Schrödinger equationMathematical analysisMathematical physicsApplied mathematicsDifferential equationPhysicsQuantum mechanicsAdvanced Mathematical Physics ProblemsNonlinear Partial Differential EquationsNonlinear Differential Equations Analysis