Existence theorems for solutions of integro-differential equations

1958 ◽  
pp. 311-318
Author(s):  
B. M. Gagaev
Keyword(s):  
Differential Equations ◽  
Existence Theorems

scholarly journals On Existence Theorems to Symmetric Functional Set-Valued Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1219
Author(s):  
Marek T. Malinowski
Keyword(s):  
Differential Equations ◽  
Existence And Uniqueness ◽  
Existence Theorems ◽  
Type Theorem ◽  
Integral Representations ◽  
Uniqueness Of The Solution ◽  
Nonempty Compact ◽  
Picard Type Theorem ◽  
Convex Subsets

In this paper, we consider functional set-valued differential equations in their integral representations that possess integrals symmetrically on both sides of the equations. The solutions have values that are the nonempty compact and convex subsets. The main results contain a Peano type theorem on the existence of the solution and a Picard type theorem on the existence and uniqueness of the solution to such equations. The proofs are based on sequences of approximations that are constructed with appropriate Hukuhara differences of sets. An estimate of the magnitude of the solution’s values is provided as well. We show the closeness of the unique solutions when the equations differ slightly.

scholarly journals Fixed point theorems of discontinuous increasing operators and applications to nonlinear integro-differential equations

2000 ◽  
Vol 158 ◽  
pp. 73-86
Author(s):  
Jinqing Zhang
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Differential Equations ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Existence Theorems ◽  
Maximal And Minimal Solutions

AbstractIn this paper, we obtain some new existence theorems of the maximal and minimal fixed points for discontinuous increasing operators in C[I,E], where E is a Banach space. As applications, we consider the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces.

Existence Theorems for Ordinary Differential Equations

1956 ◽  
Vol 40 (331) ◽  
pp. 69
Author(s):  
H. T. H. Piaggio ◽  
F. J. Murray ◽  
K. S. Miller
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Existence Theorems
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