Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 205, pp. 1-9.

Title: Existence of solutions for quasilinear elliptic equations 
       with nonlinear boundary conditions and indefinite weight
        
Authors: Guoqing Zhang (Univ. of Shanghai for Science and Tech., China)
         Xiangping Liu (Univ. of Shanghai for Science and Tech., China)
	 Sanyang Liu (Xidian Univ., Xi'an 710071, China)

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.