6 research outputs found
Bounded solutions and asymptotic stability of nonlinear difference equations in the complex plane
summary:An existence and uniqueness theorem for solutions in the Banach space of a nonlinear difference equation is given. The constructive character of the proof of the theorem predicts local asymptotic stability and gives information about the size of the region of attraction near equilibrium points
A functional-analytic method for the study of difference equations
<p/> <p>We will give the generalization of a recently developed functional-analytic method for studying linear and nonlinear, ordinary and partial, difference equations in the <inline-formula><graphic file="1687-1847-2004-537067-i1.gif"/></inline-formula> and <inline-formula><graphic file="1687-1847-2004-537067-i2.gif"/></inline-formula> spaces, <it>p</it>∈ℕ, <inline-formula><graphic file="1687-1847-2004-537067-i3.gif"/></inline-formula>. The method will be illustrated by use of two examples concerning a nonlinear ordinary difference equation known as the Putnam equation, and a linear partial difference equation of three variables describing the discrete Newton law of cooling in three dimensions.</p