Electronic Journal of Differential Equations,
Vol. 2000(2000), No. 17, pp. 1-17.

Title: Existence results for singular anisotropic elliptic 
       boundary-value problems

Author: Eun Heui Kim (Univ. of Houston, Houston, TX, USA)
  
Abstract: 
 We establish the existence of a positive solution for anisotropic singular
 quasilinear elliptic boundary-value problems. As an example 
 of the problems studied we have
  $$
  u^au_{xx}+u^bu_{yy}+\lambda(u+1)^{a+r}=0
  $$
 with zero Dirichlet boundary condition, on bounded convex domain in 
 ${\mathbb R}^2$. Here $0\leq b\leq a$, and $\lambda, r$ are positive constants.
 When $0<r<1$ (sublinear case), for each positive $\lambda$  there exists
 a positive solution. On the other hand when $r>1$ (superlinear case), 
 there exists a  positive constant $\lambda^*$ such that for $\lambda$ in 
 $(0,\lambda^*)$ there exists a positive solution, and for 
 $\lambda^*<\lambda$ there is no positive solution.

Submitted January 11, 2000. Published February 29, 2000.
Math Subject Classifications: 35J65, 35J70.
Key Words: anisotropic; singular; sublinear; superlinear; 
           elliptic boundary-value problems.