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Multi‐peak standing waves for nonlinear Schrödinger equations involving critical growth
Author(s) -
Zhang Jianjun,
do Ó João Marcos,
Yang Minbo
Publication year - 2017
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.201500074
Subject(s) - mathematics , monotonic function , nonlinear system , construct (python library) , traveling wave , schrödinger's cat , mathematical analysis , quantum mechanics , physics , computer science , programming language
For the following singularly perturbed problem − ε 2 Δ u + V ( x ) u = f ( u ) ,u ∈ H 1R N , N ≥ 3 , we construct a solution u ε which concentrates at several given isolated positive local minimum components of V as ε → 0 . Here, the nonlinearity f is of critical growth. Moreover, the monotonicity of f ( s ) / s and the so‐called Ambrosetti–Rabinowitz condition are not required.