Existence and concentration of ground state solutions for a Kirchhoff type problem
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Date
2016-01-04
Authors
Fan, Haining
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
This article concerns the Kirchhoff type problem
-(ε2α + εb ∫ℝ3|∇u|2dx)∆u + V(x)u = K(x)|u|p-1u, x ∈ ℝ3,
u ∈ H1(ℝ3),
where α, b are positive constants, 2 < p < 5, ε > 0 is a small parameter, and V(x), K(x) ∈ C1(ℝ3). Under certain assumptions on the non-constant potentials V(x) and K(x), we prove the existence and concentration properties of a positive ground state solution as ε → 0. Our main tool is a Nehari-Pohozaev manifold.
Description
Keywords
Nehari-Pohozaev manifold, Nonlocal problem, Positive solution, Concentration property
Citation
Fan, H. (2016). Existence and concentration of ground state solutions for a Kirchhoff type problem. <i>Electronic Journal of Differential Equations, 2016</i>(05), pp. 1-18.