Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff Type Problems with a General Critical Nonlinearity
Document Type
Article
Publication Date
7-17-2018
Publication Title
Proceedings of the Edinburgh Mathematical Society
Volume
61
Issue
4
First page number:
1023
Last page number:
1040
Abstract
We are concerned with the following Kirchhoff-type equation where M ∈ C(ℝ+, ℝ+), V ∈ C(ℝN, ℝ+) and f(s) is of critical growth. In this paper, we construct a localized bound state solution concentrating at a local minimum of V as ε → 0 under certain conditions on f(s), M and V. In particular, the monotonicity of f(s)/s and the Ambrosetti–Rabinowitz condition are not required.
Keywords
Kirchhoff equations, Existence and concentration, Critical growth
Language
eng
Repository Citation
Zhang, J.,
Costa, D. G.,
do O', J. M.
(2018).
Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff Type Problems with a General Critical Nonlinearity.
Proceedings of the Edinburgh Mathematical Society, 61(4),
1023-1040.
http://dx.doi.org/10.1017/S0013091518000056