Electron. J. Diff. Equ., Vol. 2015 (2015), No. 292, pp. 1-14.

Multiplicity of positive solutions for second-order differential inclusion systems depending on two parameters

Ziqing Yuan, Lihong Huang, Chunyi Zeng

Abstract:
We consider the two-point boundary-value system
$$\displaylines{ -u''_i+u_i\in\lambda\partial_{u_i}F(u_1,\ldots,u_n) +\mu\partial_{u_i}G(u_1,\ldots,u_n),\cr u'_i(a)=u'_i(b)=0\quad u_i\geq 0,\quad 1\leq i\leq n. }$$
Applying a version of nonsmooth three critical points theorem, we show the existence of at least three positive solutions.

Submitted February 20, 2015. Published November 30, 2015.
Math Subject Classifications: 49J40, 35R70, 35L85.
Key Words: Neumann problem; differential inclusion system; locally Lipschitz; nonsmooth critical point.

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Ziqing Yuan
College of Mathematics and Econometrics
Hunan University
Changsha, Hunan 410082, China
email: junjyuan@sina.com
Lihong Huang
College of Mathematics and Econometrics
Hunan University
Changsha, Hunan 410082, China
email: lhhuang@hnu.edu.cn
Chunyi Zeng
Department of Foundational Education
Southwest University for Nationalities
Chengdu, Sichuan 610000, China
email: ykbzcy@163.com

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