Multiple positive solutions for Kirchhoff type problems involving concave-convex nonlinearities

Jia-Feng Liao; Yang Pu; Xiao-Feng Ke; Chun-Lei Tang

doi:10.3934/cpaa.2017107

Article Contents

2017, Volume 16, Issue 6: 2157-2175. Doi: 10.3934/cpaa.2017107

This issue Previous Article A Heteroclinic Solution to a Variational Problem Corresponding to FitzHugh-Nagumo type Reaction-Diffusion System with Heterogeneity Next Article Boundary Layer Problem and Quasineutral Limit of Compressible Euler-Poisson System

Multiple positive solutions for Kirchhoff type problems involving concave-convex nonlinearities

1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
2.
School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, 637002, China

^* Corresponding author
^* Corresponding author

Received: December 31, 2016

Revised: March 31, 2017

Published: September 2017

supported by National Natural Science Foundation of China(No. 11471267); Natural Science Foundation of Education of Guizhou Province(No. KY[2016]046); Research Foundation of China West Normal University(No. 16E014;No. 15D006)

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Abstract

In this paper, we are interested in looking for multiple solutions for a class of Kirchhoff type problems with concave-convex nonlinearities. Under the combined effect of coefficient functions of concave-convex nonlinearities, by the Nehari method, we obtain two solutions, and one of them is a ground state solution. Under some stronger conditions, we point that the two solutions are positive solutions by the strong maximum principle.

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Mathematics Subject Classification: Primary: 35J25; Secondary: 35B50.

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