On extending existence theory from scalar ordinary differential equations to infinite quasimonotone systems of functional equations

About reducing integro-differential equations with infinite limits of integration to systems of ordinary differential equations

*Correspondence: [email protected] Department of Mathematics and Computer Sciences, Ariel University of Samaria, Ariel, Israel Abstract The purpose of this paper is to propose a method for studying integro-differential equations with infinite limits of integration. The main idea of this method is to reduce integro-differential equations to auxiliary systems of ordinary differential equations. Re...

Existence, Multiplicity, and Bifurcation in Systems of Ordinary Differential Equations

We prove new non-resonance conditions for boundary value problems for two dimensional systems of ordinary differential equations. We apply these results to the existence of solutions to nonlinear problems. We then study global bifurcation for such systems of ordinary differential equations Rotation numbers are associated with solutions and are shown to be invariant along bifurcating continua. T...

Existence and continuous dependence for fractional neutral functional differential equations

In this paper, we investigate the existence, uniqueness and continuous dependence of solutions of fractional neutral functional differential equations with infinite delay and the Caputo fractional derivative order, by means of the Banach's contraction principle and the Schauder's fixed point theorem.

Volterra integro-differential equations and infinite systems of ordinary differential equations

Inferring reaction systems from ordinary differential equations

In Mathematical Biology, many dynamical models of biochemical reaction systems are presented with Ordinary Differential Equations (ODE). Once kinetic parameter values are fixed, this simple mathematical formalism completely defines the dynamical behavior of a system of biochemical reactions and provides powerful tools for deterministic simulations, parameter sensitivity analysis, bifurcation an...