scholarly journals Existence of Solutions of Nonlinear Differential Equations with Nonlocal Conditions

2000 ◽  
Vol 252 (1) ◽  
pp. 477-483 ◽  
Author(s):  
M. Benchohra ◽  
S.K. Ntouyas
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions

scholarly journals On a Coupled System of Random and Stochastic Nonlinear Differential Equations with Coupled Nonlocal Random and Stochastic Nonlinear Integral Conditions

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2111
Author(s):  
Ahmed M. A. El-Sayed ◽  
Hoda A. Fouad
Keyword(s):  
Differential Equations ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions ◽  
Integral Condition ◽  
Coupled System ◽  
Coupled Systems ◽  
Integral Conditions ◽  
Uniqueness Of The Solution ◽  
Nonlocal Integral Condition

It is well known that Stochastic equations had many useful applications in describing numerous events and problems of real world, and the nonlocal integral condition is important in physics, finance and engineering. Here we are concerned with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

scholarly journals On a Coupled System of Random and Stochastic Differential Equations with Nonlocal Stochastic Integral Conditions

2021 ◽  
Author(s):  
A. M. A. El-Sayed ◽  
Hoda A. Foued
Keyword(s):  
Differential Equations ◽  
Continuous Dependence ◽  
Existence Of Solutions ◽  
Stochastic Integral ◽  
Nonlinear Differential Equations ◽  
Nonlocal Conditions ◽  
Coupled System ◽  
Coupled Systems ◽  
Integral Conditions ◽  
Uniqueness Of The Solution

Here we are concerning with two problems of a coupled system of random and stochastic nonlinear differential equations with two coupled systems of nonlinear nonlocal random and stochastic integral conditions. The existence of solutions will be studied. The sufficient condition for the uniqueness of the solution will be given. The continuous dependence of the unique solution on the nonlocal conditions will be proved.

scholarly journals Existence of solutions of nonlinear differential equations with deviating arguments

1991 ◽  
Vol 44 (3) ◽  
pp. 467-476
Author(s):  
K. Balachandran ◽  
S. Ilamaran
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Existence Theorem ◽  
Point Theorem ◽  
Measure Of Noncompactness ◽  
Existence Of Solutions ◽  
Nonlinear Differential Equations ◽  
Deviating Arguments ◽  
Darbo Fixed Point Theorem

We prove an existence theorem for nonlinear differential equations with deviating arguments and with implicit derivatives. The proof is based on the notion of measure of noncompactness and the Darbo fixed point theorem.

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