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

Journal Article · Sun Dec 15 00:00:00 EST 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4850835· OSTI ID:22250912

Liang, Sihua ^[1]; Shi, Shaoyun ^[2]

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1. College of Mathematics, Changchun Normal University, Changchun 130032, Jilin (China)
2. College of Mathematics, Jilin University, Changchun 130012 (China)

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}.

• OSTI ID: 22250912
• Journal Information: Journal of Mathematical Physics, Vol. 54, Issue 12; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICAL METHODS AND COMPUTING
CRITICAL FREQUENCY
FUNCTIONS
MATHEMATICAL SOLUTIONS
TRAPPING
VARIATIONAL METHODS