On the existence of positive solutions of quasilinear elliptic boundary value problems

Authors

Eun Heui Kim, University of Connecticut

Date of Completion

January 1999

Keywords

Mathematics

Degree

Ph.D.

Abstract

We establish the existence of a positive solution of a class of anisotropic singular quasilinear elliptic boundary value problems with certain nonlinearities. One example is: u^auxx+u^buyy +lu+1^a+r =0,u&vbm0; 6W=0. 1 Here Ω is a bounded convex smooth domain in R₂, a ≥ b ≥ 0, λ > 0, and r > 0. ^ If 0 < r < 1 (sublinear case), then (1) has a solution for all λ > 0. On the other hand, if r > 1 (superlinear case), then there exists a positive constant λ* such that for each λ ∈ (0, λ*], (1) has a positive solution. ^ Finally, we present some numerical results for some open theoretical questions for these types of problems. ^

Recommended Citation

Kim, Eun Heui, "On the existence of positive solutions of quasilinear elliptic boundary value problems" (1999). Doctoral Dissertations. AAI9930653.
https://digitalcommons.lib.uconn.edu/dissertations/AAI9930653