Existence Results for Singular Anisotropic Elliptic Boundary-value Problems
Date
2000-02-29
Authors
Kim, Eun Heui
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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
uα uxx+ ub uyy + λ (u + 1)α+r = 0
with zero Dirichlet boundary condition, on a bounded convex domain in ℝ2. Here 0 ≤ b ≤ α, and λ, r are positive constants. When 0 < r < 1 (sublinear case), for each positive λ there exists a positive solution. On the other hand when r > 1 (superlinear case), there exists a positive constant λ* such that for λ in (0, λ*) there exists a positive solution, and for λ* < λ there is no positive solution.
Description
Keywords
Anisotropic, Singular, Sublinear, Superlinear, Elliptic boundary-value problems
Citation
Kim, E. H. (2000). Existence results for singular anisotropic elliptic boundary-value problems. <i>Electronic Journal of Differential Equations, 2000</i>(17), pp. 1-17.
Rights
Attribution 4.0 International
Rights Holder
This work is licensed under a Creative Commons Attribution 4.0 International License.