scholarly journals Structural Operators and Eigenmanifold Decomposition for Functional Differential Equations in Hilbert Spaces

1996 ◽  
Vol 204 (2) ◽  
pp. 554-581 ◽  
Author(s):  
Shin-ichi Nakagiri ◽  
Hiroki Tanabe
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Functional Differential Equations ◽  
Functional Differential

scholarly journals Nonlinear variational evolution inequalities in Hilbert spaces

2000 ◽  
Vol 23 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Jin-Mun Jeong ◽  
Doo-Hoan Jeong ◽  
Jong-Yeoul Park
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Nonlinear Term ◽  
Functional Differential Equations ◽  
Nonlinear Functional ◽  
Coercive Operator ◽  
Functional Differential ◽  
Variational Evolution

The regular problem for solutions of the nonlinear functional differential equations with a nonlinear hemicontinuous and coercive operatorAand a nonlinear termf(.,.):x′(t)+Ax(t)+∂ϕ(x(t))∋f(t,x(t))+h(t)is studied. The existence, uniqueness, and a variation of solutions of the equation are given.

scholarly journals Hölder Continuous Regularity of Stochastic Convolutions with Distributed Delay

2021 ◽  
Author(s):  
Kai Liu
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Functional Differential Equations ◽  
Distributed Delay ◽  
Fundamental Solutions ◽  
Regularity Property ◽  
Hölder Continuous ◽  
Stochastic Convolutions ◽  
Retarded Functional Differential Equations ◽  
Functional Differential

AbstractIn this work, we consider the Hölder continuous regularity of stochastic convolutions for a class of linear stochastic retarded functional differential equations with distributed delay in Hilbert spaces. By focusing on distributed delays, we first establish some more delicate estimates for fundamental solutions than those given in Liu (Discrete Contin. Dyn. Syst. Ser. B 25(4), 1279–1298, 2020). Then we apply these estimates to stochastic convolutions incurred by distributed delay to study their regularity property. Last, we present some easily-verified results by considering the regularity of a class of systems whose delay operators have the same order derivatives as those in instantaneous ones.

scholarly journals Control Problems for Semilinear Neutral Differential Equations in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin-Mun Jeong ◽  
Seong Ho Cho
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Approximate Controllability ◽  
Functional Differential Equations ◽  
Fractional Power ◽  
Regularity Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Neutral Equations ◽  
Neutral Differential Equations ◽  
Functional Differential

We construct some results on the regularity of solutions and the approximate controllability for neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the controllability of the neutral equations, we first consider the existence and regularity of solutions of the neutral control system by using fractional power of operators and the local Lipschitz continuity of nonlinear term. Our purpose is to obtain the existence of solutions and the approximate controllability for neutral functional differential control systems without using many of the strong restrictions considered in the previous literature. Finally we give a simple example to which our main result can be applied.

scholarly journals On nondensely defined semilinear stochastic functional differential equations with nonlocal conditions

2006 ◽  
Vol 2006 ◽  
pp. 1-13 ◽  
Author(s):  
M. Benchohra ◽  
S. K. Ntouyas ◽  
A. Ouahab
Keyword(s):  
Differential Equations ◽  
Hilbert Spaces ◽  
Existence Of Solutions ◽  
Functional Differential Equations ◽  
Nonlocal Conditions ◽  
Stochastic Functional Differential Equations ◽  
First Order ◽  
Nonlinear Alternative ◽  
Functional Differential ◽  
Stochastic Functional

The nonlinear alternative of Leray-Schauder type is used to investigate the existence of solutions for first-order semilinear stochastic functional differential equations in Hilbert spaces.

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