On the existence of ground states of an equation of Schrödinger–Poisson–Slater type
Chun‐Yu Lei, Yutian Lei
Abstract
We study the existence of ground states of a Schrödinger–Poisson–Slater type equation with pure power nonlinearity. By carrying out the constrained minimization on a special manifold, which is a combination of the Pohozaev manifold and Nehari manifold, we obtain the existence of ground state solutions of this system.
Topics & Concepts
MathematicsNehari manifoldManifold (fluid mechanics)Ground stateType (biology)Schrödinger's catNonlinear systemPoisson's equationSchrödinger equationPower (physics)Mathematical analysisMathematical physicsQuantum mechanicsPhysicsEcologyEngineeringMechanical engineeringBiologyNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringNonlinear Differential Equations Analysis