Existence of solutions of nonlinear integrodifferential equations of sobolev type with nonlocal condition in Banach spaces

2000 ◽  
Vol 110 (2) ◽  
pp. 225-232 ◽  
Author(s):  
K. Balachandran ◽  
K. Uchiyama
Keyword(s):  
Banach Spaces ◽  
Existence Of Solutions ◽  
Nonlocal Condition ◽  
Integrodifferential Equations ◽  
Sobolev Type

scholarly journals Existence of solutions for impulsive fractional integrodifferential equations involving Gronwall’s inequality in Banach spaces

2012 ◽  
Vol 21 (2) ◽  
pp. 115-122
Author(s):  
A. AL-OMARI ◽  
◽  
M. H. M. RASHID ◽  
K. KARTHIKEYAN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fractional Calculus ◽  
Banach Spaces ◽  
Caputo Derivative ◽  
Existence Of Solutions ◽  
Sufficient Conditions ◽  
Fixed Point Method ◽  
Integrodifferential Equations ◽  
Gronwall’S Inequality ◽  
Mild Conditions

In this paper, we study boundary value problems for impulsive fractional integrodifferential equations involving Caputo derivative in Banach spaces. A generalized singular type Gronwall inequality is given to obtain an important priori bounds. Some sufficient conditions for the existence solutions are established by virtue of fractional calculus and fixed point method under some mild conditions.

scholarly journals Existence of solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces

2003 ◽  
Vol 16 (2) ◽  
pp. 163-170 ◽  
Author(s):  
M. Kanakaraj ◽  
K. Balachandran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Mild Solutions ◽  
Topological Spaces ◽  
Sobolev Type ◽  
Multivalued Maps ◽  
Locally Convex

The existence of mild solutions of Sobolev-type semilinear mixed integrodifferential inclusions in Banach spaces is proved using a fixed point theorem for multivalued maps on locally convex topological spaces.

scholarly journals Existence of Solutions of a Class of Abstract Second Order Nonlinear Integrodifferential Equations

2002 ◽  
Vol 15 (2) ◽  
pp. 115-124 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Cosine Families ◽  
Schaefer Fixed Point Theorem ◽  
Families Of Operators

In this paper we prove the existence of solutions of nonlinear second order integrodifferential equations in Banach spaces. The results are obtained by using the theory of strongly continuous cosine families of operators and the Schaefer fixed point theorem.

scholarly journals Existence of solutions and controllability of nonlinear integrodifferential systems in Banach spaces

2003 ◽  
Vol 2003 (2) ◽  
pp. 65-79 ◽  
Author(s):  
K. Balachandran ◽  
J. Y. Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Point Theorem ◽  
Existence Of Solutions ◽  
Nonlocal Conditions ◽  
Sufficient Conditions ◽  
Strong Solutions ◽  
Integrodifferential Equations ◽  
Schäuder Fixed Point Theorem

We prove the existence of mild and strong solutions of integrodifferential equations with nonlocal conditions in Banach spaces. Further sufficient conditions for the controllability of integrodifferential systems are established. The results are obtained by using the Schauder fixed-point theorem. Examples are provided to illustrate the theory.

scholarly journals EXISTENCE RESULTS FOR NEUTRAL IMPULSIVE QUASILINEAR MIXED VOLTERRA-FREDHOLM TYPE INTEGRODIFFERENTIAL SYSTEMS

2020 ◽  
pp. 83-92
Author(s):  
NARESH KUMAR JOTHI ◽  
K. A. VENKATESAN ◽  
T. GUNASEKAR ◽  
F. PAUL SAMUEL
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Semigroup Theory ◽  
Existence Results ◽  
Integrodifferential Equations ◽  
Fredholm Type ◽  
Impulsive Conditions ◽  
Fixed Point Technique

The paper deals with the study of existence of solutions for quasilinear neutral mixed Volterra-Fredholm-type integrodifferential equations with nonlocal and impulsive conditions in Banach spaces. The results are obtained by using a fixed point technique and semigroup theory

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