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Multiple solutions for a modified Kirchhoff‐type equation in R N
Author(s) -
Feng ZongHong,
Wu Xian,
Li HongXu
Publication year - 2014
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.3102
Subject(s) - mathematics , type (biology) , sequence (biology) , mathematical physics , perturbation (astronomy) , mathematical analysis , pure mathematics , combinatorics , physics , quantum mechanics , chemistry , ecology , biochemistry , biology
In this paper, we study the following modified Kirchhoff‐type equations of the form: − a + b ∫ R N | ∇ u | 2 dx △ u − u △ u 2 + V ( x ) u = h ( x , u ) , x ∈ R N ,where a > 0, b ≥ 0, h ∈ CR N × R , Rand V ∈ CR N , R . Under appropriate assumptions on V ( x ) and h ( x , u ), some existence results for positive solutions, negative solutions, and sequence of high energy solutions are obtained via a perturbation method. Copyright © 2014 John Wiley & Sons, Ltd.
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