Extinction in a nonautonomous system of Volterra integrodifferential equations

Extinction in Nonautonomous Competitive Lotka-volterra Systems

It is well known that for the two species autonomous competitive Lotka-Volterra model with no fixed point in the open positive quadrant, one of the species is driven to extinction, whilst the other population stabilises at its own carrying capacity. In this paper we prove a generalisation of this result to nonautonomous systems of arbitrary finite dimension. That is, for the n species nonautono...

Extinction of Species in Nonautonomous Lotka-volterra Systems

A nonautonomous nth order Lotka-Volterra system of differential equations is considered. It is shown that if the coefficients satisfy certain inequalities, then any solution with positive components at some point will have all of its last n − 1 components tend to zero, while the first one will stabilize at a certain solution of a logistic equation.

Solvability of Nonautonomous Fractional Integrodifferential Equations with Infinite Delay

Ulam stabilities for nonlinear Volterra-Fredholm delay integrodifferential equations

In the present research paper we derive results about existence and uniqueness of solutions and Ulam--Hyers and Rassias stabilities of nonlinear Volterra--Fredholm delay integrodifferential equations. Pachpatte's inequality and Picard operator theory are the main tools that are used to obtain our main results. We concluded this work with applications of ob...

Weak Solutions for a Class of Parabolic Volterra Integrodifferential Equations

u’(t)+Au(t)= ‘a(t,s)g(s,u(s))ds+f(t,U(t)), I 120, 0 u(0) = 0. The operator A is the negative infinitesimal generator of an analytic semigroup in a Banach space X. The operator g(t, u) is related to A by a special form g(t, a) = A”*q(t, u), where q(t, u) is an appropriate “lower order” operator. We show the existence and uniqueness of weak solutions and their continuability to infinity under sui...