Extremal solutions and comparison principle for nonlinear integro-differential equations in a Banach space

1993 ◽  
Vol 9 (2) ◽  
pp. 152-159
Author(s):  
Chen Yubo ◽  
Zhuang Wan
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Comparison Principle ◽  
Extremal Solutions

scholarly journals Solvability of discontinuous functional differential systems in l∞(M)

2006 ◽  
Vol 48 (2) ◽  
pp. 237-243
Author(s):  
A. Cabada ◽  
J. Ángel Cid ◽  
S. Heikkilä
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Infinite System ◽  
Functional Differential Equations ◽  
Extremal Solutions ◽  
Differential Systems ◽  
First Order ◽  
Functional Differential Systems ◽  
Bounded Functions ◽  
Functional Differential

AbstractWe study the existence of extremal solutions for an infinite system of first-order discontinuous functional differential equations in the Banach space of the bounded functions I∞(M).

scholarly journals Basic theory of differential equations with linear perturbations of second type on time scales

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yige Zhao ◽  
Yibing Sun ◽  
Zhi Liu ◽  
Zhanbing Bai
Keyword(s):  
Differential Equations ◽  
Existence Theorem ◽  
Time Scales ◽  
Comparison Principle ◽  
Basic Theory ◽  
Extremal Solutions ◽  
Differential Inequalities ◽  
Linear Perturbations ◽  
Lipschitz Conditions

AbstractIn this paper, we develop the theory of differential equations with linear perturbations of second type on time scales. An existence theorem for differential equations with linear perturbations of second type on time scales is given under $\mathscr{D}$D-Lipschitz conditions. Some fundamental differential inequalities on time scales, which are utilized to investigate the existence of extremal solutions, are also presented. The comparison principle on differential equations with linear perturbations of second type on time scales is established. Our results in this paper extend and improve some well-known results.

Differential equations with causal operators in a Banach space

2005 ◽  
Vol 62 (2) ◽  
pp. 301-313 ◽  
Author(s):  
Z. Drici ◽  
F.A. McRae ◽  
J. Vasundhara Devi
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Causal Operators

scholarly journals Asymptotic equivalence of impulsive differential equations in a Banach space

1990 ◽  
Vol 34 ◽  
pp. 249-257 ◽  
Author(s):  
D. D. Bainov ◽  
S. I. Kostadinov ◽  
A. D. Myshkis
Keyword(s):  
Banach Space ◽  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Asymptotic Equivalence
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