Electron. J. Diff. Equ., Vol. 2015 (2015), No. 316, pp. 1-14.

Multiple positive solutions for superlinear Kirchhoff type problems on R^N

Yu Duan, Chun-Lei Tang

Abstract:
In this article, we study the multiplicity of positive solutions for a class of Kirchhoff type problems depending on two real functions and a nonnegative parameter on an unbounded domain. Using the variational method and iterative techniques, we show that if the nonlinearity is subcritical and superlinear at zero and infinity, then the Kirchhoff type problems admits at least two positive solutions when the parameter is sufficiently small.

Submitted August 28, 2015. Published December 28, 2015.
Math Subject Classifications: 35R09, 35A15, 35B09.
Key Words: Kirchhoff type problems; Pohozaev identity; variational method; iterative technique.

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Yu Duan
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: duanyu3612@163.com
Chun-Lei Tang
School of Mathematics and Statistics
Southwest University
Chongqing 400715, China
email: tangcl@swu.edu.cn, tangcl8888@sina.com

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