TY - JOUR
T1 - Multiplicity of positive solutions of nonlinear Schrödinger equations concentrating at a potential well
AU - Cingolani, Silvia
AU - Jeanjean, Louis
AU - Tanaka, Kazunaga
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2014.
PY - 2015/5
Y1 - 2015/5
N2 - We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.
AB - We consider singularly perturbed nonlinear Schrödinger equations (Formula Presented) where (Formula Presented) and f is a nonlinear term which satisfies the so-called Berestycki–Lions conditions. We assume that there exists a bounded domain (Formula Presented) such that (Formula Presented) and we set (Formula Presented). For (Formula Presented) small we prove the existence of at least (Formula Presented) solutions to (0.1) concentrating, as (Formula Presented) around K. We remark that, under our assumptions of f, the search of solutions to (0.1) cannot be reduced to the study of the critical points of a functional restricted to a Nehari manifold.
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U2 - 10.1007/s00526-014-0754-5
DO - 10.1007/s00526-014-0754-5
M3 - Article
AN - SCOPUS:84939891674
SN - 0944-2669
VL - 53
SP - 413
EP - 439
JO - Calculus of Variations and Partial Differential Equations
JF - Calculus of Variations and Partial Differential Equations
IS - 1-2
ER -