Normalized ground state for the Sobolev critical Schrödinger equation involving Hardy term with combined nonlinearities
Houwang Li, Wenming Zou
Abstract
Abstract In this paper, we study the existence and properties of normalized solutions for the following Sobolev critical Schrödinger equation involving Hardy term: with prescribed mass where 2* is the Sobolev critical exponent. For a L 2 ‐subcritical, L 2 ‐critical, or L 2 ‐supercritical perturbation , we prove several existence results of normalized ground state when and non‐existence results when . Furthermore, we also consider the asymptotic behavior of the normalized solutions u as or .
Topics & Concepts
Sobolev spaceMathematicsSupercritical fluidTerm (time)Ground statePerturbation (astronomy)Critical exponentMathematical analysisExponentSchrödinger equationMathematical physicsPhysicsQuantum mechanicsGeometryScalingThermodynamicsPhilosophyLinguisticsAdvanced Mathematical Physics ProblemsNonlinear Partial Differential EquationsSpectral Theory in Mathematical Physics