scholarly journals The existence and compactness of the set of solutions for a nonlinear integrodifferential equation in N variables in a Banach space

2020 ◽  
Keyword(s):  
Banach Space ◽  
Integrodifferential Equation ◽  
Nonlinear Integrodifferential Equation

scholarly journals Existence Results for an Impulsive Neutral Fractional Integrodifferential Equation with Infinite Delay

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Alka Chadha ◽  
Dwijendra N. Pandey
Keyword(s):  
Banach Space ◽  
Mild Solution ◽  
Hausdorff Measure ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Existence Results ◽  
Hausdorff Measure Of Noncompactness ◽  
Arbitrary Banach Space ◽  
Fractional Integrodifferential Equation

We consider an impulsive neutral fractional integrodifferential equation with infinite delay in an arbitrary Banach spaceX. The existence of mild solution is established by using solution operator and Hausdorff measure of noncompactness.

scholarly journals Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Aneta Sikorska-Nowak
Keyword(s):  
Banach Space ◽  
Boundary Conditions ◽  
Banach Spaces ◽  
Integrodifferential Equation ◽  
Measure Of Noncompactness ◽  
Existence Theorems ◽  
Integrodifferential Equations ◽  
Existence Theory

We prove existence theorems for the integrodifferential equationx'(t)=f(t,x(t),∫0tk(t,s,x(s))ds),x(0)=x0,t∈Ia=[0,a],a>0, wheref,k,xare functions with values in a Banach spaceEand the integral is taken in the sense of HL. Additionally, the functionsfandksatisfy certain boundary conditions expressed in terms of the measure of noncompactness.

scholarly journals On an abstract nonlinear second order integrodifferential equation

2007 ◽  
Vol 5 (2) ◽  
pp. 167-174 ◽  
Author(s):  
M. B. Dhakne ◽  
G. B. Lamb
Keyword(s):  
Banach Space ◽  
Global Existence ◽  
Integrodifferential Equation ◽  
Existence Of Solutions ◽  
A Priori ◽  
Second Order ◽  
A Priori Bounds ◽  
Global Existence Of Solutions

The aim of the present paper is to study the global existence of solutions of nonlinear second order integrodifferential equation in Banach space. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.

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