Title

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

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