In this paper we consider the question of uniqueness of positive solutions for Dirichlet problems of the form - Δ u(x)= g(λ,u(x)) in B, u(x) = 0 on ϑB,
where A is the Laplace operator, B is the unit ball in RˆN, and A>0. We show that if g(λ,u)=uˆ(N+2)/(N-2) + λ, that is g has "critical growth", then large positive solutions are unique. We also prove uniqueness of large solutions when g(λ,u)=A f(u) with f(0) < 0, f "superlinear" and monotone. We use a number of methods from nonlinear functional analysis such as variational identities, Sturm comparison theorems and methods of order.
We also present a regularity result on linear elliptic equation where a coefficient has critical growth.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc330654 |
| Date | 12 1900 |
| Creators | Ali, Ismail, 1961- |
| Contributors | Castro, Alfonso, 1950-, Neuberger, John W., Warchall, Henry Alexander, Renka, Robert J. |
| Publisher | University of North Texas |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 50 leaves : ill., Text |
| Rights | Public, Ali, Ismail, 1961-, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
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