1. CMB 2017 (vol 60 pp. 436)
||Globally Asymptotic Stability of a Delayed Integro-Differential Equation with Nonlocal Diffusion|
We study a population model with nonlocal diffusion, which
is a delayed integro-differential equation with double nonlinearity
and two integrable kernels. By comparison method and analytical
technique, we obtain globally asymptotic stability of the zero
solution and the positive equilibrium. The results obtained
reveal that the globally asymptotic stability only depends on
the property of nonlinearity. As application, an example for
a population model with age structure is discussed at the end
of the article.
Keywords:integro-differential equation, nonlocal diffusion, equilibrium, globally asymptotic stability, population model with age structure
Categories:45J05, 35K57, 92D25
2. CMB 2014 (vol 58 pp. 174)
||Periodic Solutions of Almost Linear Volterra Integro-dynamic Equation on Periodic Time Scales|
Using Krasnoselskii's fixed point theorem, we deduce
the existence of periodic solutions of nonlinear system of integro-dynamic
equations on periodic time scales. These equations are
studied under a set of assumptions on the functions involved
equations. The equations will be called almost linear when these
assumptions hold. The results of this papers are new for the
continuous and discrete time scales.
Keywords:Volterra integro-dynamic equation, time scales, Krasnoselsii's fixed point theorem, periodic solution
3. CMB 2011 (vol 56 pp. 80)
||Three Fixed Point Theorems: Periodic Solutions of a Volterra Type Integral Equation with Infinite Heredity|
In this paper we study the existence of periodic solutions of a Volterra type integral equation with infinite heredity. Banach fixed point theorem, Krasnosel'skii's fixed point theorem, and a combination of Krasnosel'skii's
and Schaefer's fixed point theorems are employed in the analysis.
The combination theorem of Krasnosel'skii and Schaefer requires an a priori bound on all solutions.
We employ Liapunov's direct method to obtain such an a priori bound.
In the process, we compare these theorems in terms of assumptions and outcomes.
Keywords:Volterra integral equation, periodic solutions, Liapunov's method, Krasnosel'skii's fixed point theorem, Schaefer's fixed point theorem