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

## 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^{a}uxx+u^{b}uyy +lu+1^{a+r} =0,u&vbm0; 6W=0. 1 Here Ω is a bounded convex smooth domain in * R*_{2}, *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