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Standing waves for nonlinear Schrödinger equations involving critical growth
Author(s) -
Zhang Jianjun,
Chen Zhijie,
Zou Wenming
Publication year - 2014
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdu054
Subject(s) - nonlinear system , mathematics , construct (python library) , component (thermodynamics) , mathematical physics , mathematical analysis , physics , thermodynamics , quantum mechanics , computer science , programming language
We consider the following singularly perturbed nonlinear elliptic problem:- ε 2 Δ u + V ( x ) u = f ( u ) , u ∈ H 1 ( R N ) ,where N ⩾ 3 and f is the nonlinearity of critical growth . In this paper, we construct a solution u ε of the above problem, which concentrates at an isolated component of the positive local minimum points of V as ε → 0 under certain conditions on f . Our result completes the study made in some very recent works in the sense that, in those papers, only the subcritical growth was considered.