Existence and Concentration of Positive Solutions for Nonlinear Kirchhoff Type Problems with a General Critical Nonlinearity

Authors

Jianjun Zhang, Chongqing Jiaotong UniversityFollow
David G. Costa, University of Nevada, Las VegasFollow
Joao Marcos do O', Federal University of Paraiba

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