Xiaofei Cao, Junxiang Xu, Jun Wang
Abstract:
In this article, we consider the multiplicity of positive solutions for
a class of Kirchhoff type problems with concave and convex nonlinearities.
Under appropriate assumptions, we prove that the problem has at least
two positive solutions, moreover, one of which is a positive ground
state solution. Our approach is mainly based on the Nehari manifold,
Ekeland variational principle and the theory of Lagrange multipliers.
Submitted July 25, 2016. Published November 25, 2016.
Math Subject Classifications: 35A01, 35A15.
Key Words: Kirchhoff type problem; Ekeland variational principle;
Nehari manifold.
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Xiaofei Cao Department of Mathematics Southeast University Nanjing, Jiangsu 210096, China email: caoxiaofei258@126.com |
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Junxiang Xu Department of Mathematics Southeast University Nanjing, Jiangsu 210096, China email: xujun@seu.edu.cn |
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Jun Wang Faculty of Science Jiangsu University Zhenjiang, Jiangsu 212013, China email: wangmath2011@126.com |
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