Multiplicity of Positive Solutions and the Method of Upper and Lower Solutions for Nonlinear Elliptic Pdes
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Date
2021-10-19
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Addis Ababa University
Abstract
In this paper, we are interested in the positive solutions of nonlinear elliptic
boundary value problems on a bounded domain. We establish the existence,
uniqueness and multiplicity of positive solutions for the nonlinear elliptic
boundary value problem of autonomous type,
(
Lu = f (x, u) in W
Bu = c(x) on ¶W
and then proceed to establish conditions for existence and uniqueness of positive
global solutions for the non-autonomous type elliptic BVP,
8><
>:
ut 4u = f (x, t, u) in D
Bu = c(x, t) on ¶D
u(x, 0) = u0(x) in W
We employ the method of lower and upper solutions along with the monotone
iterative techniques to this end.
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Keywords
Multiplicity, Positive Solutions, Method of Upper and Lower Solutions, Nonlinear Elliptic PDEs