Systems by the Method of Quasisolutions
Abstract
**Please note that the full text is embargoed** ABSTRACT: Recently [10] the method of lower and upper solutions has been
extended to systems of reaction diffusion equations which has
become very useful in dealing with applications. This extension
depends crucially on a certain property known as quasimonotone
nondecreasing property [8] without which the results fail under
natural definition of lower and upper solutions. When the
quasimonotone property does not hold but a certain mixed
quasimonotone property is satisfied, which is the case in several
applications [7], the method of quasisolutions is more suitable
[2,4,6,9]. All these results utilize monotone iterative technique.
When no monotone condition holds one can also get just existence
results [5] assuming Müller's type of lower and upper solutions.
However in this case monotone technique fails.
In this paper, we discuss the asymptotic stability of the
stationary solution of reaction-diffusion systems. We employ the
method of quasisolutions and monotone technique.