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Positive solutions for asymptotically linear Schrödinger–Kirchhoff‐type equations
Author(s) -
Liu Zhisu,
Guo Shangjiang
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2815
Subject(s) - mathematics , infinity , type (biology) , focus (optics) , mathematical analysis , mathematical physics , physics , optics , ecology , biology
In this paper, we focus on the Schrödinger–Kirchhoff‐type equation SK − a + b ∫R 3| ∇ u | 2 dx △ u + V ( x ) u = f ( x , u ) , in R 3where a , b > 0 are constants, V : R 3 → R may not be radially symmetric, and f ( x , u ) is asymptotically linear with respect to u at infinity. Under some technical assumptions on V and f , we prove that the problem (SK) has a positive solution. Copyright © 2013 John Wiley & Sons, Ltd.