Singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities

被引：7
|
作者：
Maia, Liliane A. [1 ]
Montefusco, Eugenio [2 ]
Pellacci, Benedetta [3 ]
机构：
[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil
[2] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[3] Univ Napoli Parthenope, Ctr Direz Isola C4, DiST Dipartimento Sci & Tecnol, I-80143 Naples, Italy
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2015年 / 116卷
关键词：
Schrodinger equations; Saturable media; Concentration phenomena; Singularly perturbed elliptic equation; Asymptotically linear nonlinearities; Penalization methods; SCHRODINGER-EQUATIONS; GROUND-STATES; BOUND-STATES; SEMICLASSICAL STATES; POTENTIALS;
D O I：
10.1016/j.na.2014.09.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a class of singularly perturbed elliptic problems with nonautonomous asymptotically linear nonlinearities. The dependence on the spatial coordinates comes from the presence of a potential and of a function representing a saturation effect. We investigate the existence of nontrivial nonnegative solutions concentrating around local minima of both the potential and of the saturation function. Necessary conditions to locate the possible concentration points are also given. (C) 2014 Elsevier Ltd. All rights reserved.
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页码：193 / 209
页数：17
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