Electron. J. Diff. Equ., Vol. 2012 (2012), No. 205, pp. 1-9.

Existence of solutions for quasilinear elliptic equations with nonlinear boundary conditions and indefinite weight

Guoqing Zhang, Xiangping Liu, Sanyang Liu

Abstract:
In this article, we establish the existence and non-existence of solutions for quasilinear equations with nonlinear boundary conditions and indefinite weight. Our proofs are based on variational methods and their geometrical features. In addition, we prove that all the weak solutions are in $C^{1,\beta}(\overline{\Omega})$ for some $\beta\in(0,1)$.

Submitted June 18, 2012. Published November 24, 2012.
Math Subject Classifications: 35J60, 35P30.
Key Words: Regularity; existence; nonlinear boundary conditions; indefinite weight.

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Guoqing Zhang
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: shzhangguoqing@126.com
Xiangping Liu
College of Science
University of Shanghai for Science and Technology
Shanghai 200093, China
email: Liuxp83355650@yeah.net
Sanyang Liu
Department of Applied Mathematics
Xidian University
Xi'an 710071, China
email: liusanyang@126.com

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