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 $01$ (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.