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Title: Existence of multi-bump solutions for a class of Kirchhoff type problems in R{sup 3}

Using variational methods, we establish existence of multi-bump solutions for a class of Kirchhoff type problems −(a+b∫{sub R{sup 3}}|∇u|{sup 2}dx)Δu+λV(x)u=f(u), where f is a continuous function with subcritical growth, V(x) is a critical frequency in the sense that inf{sub x∈R{sup 3}}V(x)=0. We show that if the zero set of V(x) has several isolated connected components Ω{sub 1}, …, Ω{sub k} such that the interior of Ω{sub i} is not empty and ∂Ω{sub i} is smooth, then for λ > 0 large there exists, for any non-empty subset J ⊂ (1, …, k), a bump solution is trapped in a neighborhood of ∪{sub j∈J}Ω{sub j}.
Authors:
 [1] ;  [2] ;  [3] ;  [2]
  1. College of Mathematics, Changchun Normal University, Changchun 130032, Jilin (China)
  2. (China)
  3. College of Mathematics, Jilin University, Changchun 130012 (China)
Publication Date:
OSTI Identifier:
22250912
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; CRITICAL FREQUENCY; FUNCTIONS; MATHEMATICAL SOLUTIONS; TRAPPING; VARIATIONAL METHODS