Infinitely many positive solutions for nonlinear equations with non-symmetric potentials

• Published in: Calculus of variations and partial differential equations Vol. 51; no. 3-4; pp. 761 - 798
• Main Authors: Ao, Weiwei, Wei, Juncheng
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014; Springer Nature B.V
• Subjects: Analysis; Calculus of variations; Calculus of Variations and Optimal Control; Optimization; Control; Decay; Energy methods; Mathematical analysis; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Nonlinear equations; Nonlinearity; Schrodinger equation; Schroedinger equation; Systems Theory; Texts; Theoretical; 35J20; 35J60; 35B09

We consider the following nonlinear Schrödinger equation Δ u - ( 1 + δ V ) u + f ( u ) = 0 in R N , u > 0 in R N , u ∈ H 1 ( R N ) where V is a continuous potential and f ( u ) is a nonlinearity satisfying some decay condition and some non-degeneracy condition, respectively. Using localized energ...