Electron. J. Diff. Eqns., Vol. 2000(2000), No. 17, pp. 1-17.
### Existence results for singular anisotropic elliptic
boundary-value problems

Eun Heui Kim

**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

with zero Dirichlet boundary condition, on a bounded convex domain in
. Here
, and
,
*r* are positive constants.
When *0< r< 1* (sublinear case), for each positive
there exists a positive solution. On the other hand when
*r>1* (superlinear case),
there exists a positive constant
such that for
in
there exists a positive solution, and for
<
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.

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Eun Heui Kim

Department of Mathematics, University of Houston

Houston, TX 77204-3476 USA

email: ehkim@math.uh.edu

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