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.
引用
收藏
页码：193 / 209
页数：17
相关论文
共 50 条
  • [31] Singularly Perturbed Oscillators with Exponential Nonlinearities
    Jelbart, S.
    Kristiansen, K. U.
    Szmolyan, P.
    Wechselberger, M.
    JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2022, 34 (03) : 1823 - 1875
  • [32] NONLINEAR FOURTH ORDER PROBLEMS WITH ASYMPTOTICALLY LINEAR NONLINEARITIES
    Ben Ali, Abir Amor
    Dammak, Makkia
    MATHEMATICA BOHEMICA, 2024, 149 (02): : 209 - 223
  • [33] Singularly Perturbed Oscillators with Exponential Nonlinearities
    S. Jelbart
    K. U. Kristiansen
    P. Szmolyan
    M. Wechselberger
    Journal of Dynamics and Differential Equations, 2022, 34 : 1823 - 1875
  • [34] Asymptotically linear elliptic problems at resonance.
    Masiello, A
    Pisani, L
    ANNALI DI MATEMATICA PURA ED APPLICATA, 1996, 171 : 1 - 13
  • [35] On a class of asymptotically linear elliptic problems in RN
    Costa, DG
    Tehrani, H
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 173 (02) : 470 - 494
  • [36] A note on asymptotically linear elliptic problems in RN
    Tehrani, HT
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 271 (02) : 546 - 554
  • [37] Singularly perturbed elliptic systems
    Alves, CO
    Soares, SHM
    NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2006, 64 (01) : 109 - 129
  • [38] Supercritical elliptic problem with nonautonomous nonlinearities
    Gladiali, Francesca
    Grossi, Massimo
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (09) : 2616 - 2645
  • [39] SINGULARLY PERTURBED LINEAR BOUNDARY-VALUE-PROBLEMS
    KATHIRKAMANAYAGAN, M
    LADDE, GS
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 168 (02) : 430 - 459
  • [40] Solutions of elliptic problems with nonlinearities of linear growth
    Liu, Zhaoli
    Su, Jiabao
    Wang, Zhi-Qiang
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2009, 35 (04) : 463 - 480
12345