Normalized solutions for Schrödinger equations with critical Sobolev exponent and perturbations of Choquard terms
Peng Jin, Heng Yang, Xin’ao Zhou
Abstract
In this paper, we consider the following Schrödinger equation with perturbations of Choquard terms: [Formula: see text] where [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is the Riesz potential with order [Formula: see text]. The main results in this paper are the following: (1) existence of ground state solution with negative energy for all [Formula: see text]; (2) existence of mountain-pass solution with positive energy for all [Formula: see text]; (3) existence of ground state solution for [Formula: see text] and some [Formula: see text].
Topics & Concepts
Sobolev spaceMathematicsCritical exponentSchrödinger equationExponentSchrödinger's catMathematical analysisMathematical physicsGeometryScalingPhilosophyLinguisticsSpectral Theory in Mathematical PhysicsDifferential Equations and Boundary Problems