A Version of the Chain Rule and Integrodifferential Equations in Hilbert Spaces

1982 ◽  
Vol 13 (5) ◽  
pp. 801-810 ◽  
Author(s):  
Hans Engler
Keyword(s):  
Hilbert Spaces ◽  
Integrodifferential Equations ◽  
Chain Rule

scholarly journals Rothe's method to semilinear hyperbolic integrodifferential equations

1990 ◽  
Vol 3 (4) ◽  
pp. 245-252 ◽  
Author(s):  
D. Bahaguna ◽  
A. K. Pani ◽  
V. Raghavendra
Keyword(s):  
Strong Solution ◽  
Hilbert Spaces ◽  
Integrodifferential Equations ◽  
Unique Strong Solution ◽  
Rothe's Method ◽  
Rothe’S Method

In this paper we consider an application of Rothe's method to abstract semi-linear hyperbolic integrodifferential equations in Hilbert spaces. With the aid of Rothe's method we establish the existence of a unique strong solution.

Asymptotic behavior of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2727-2748
Author(s):  
Zuomao Yan ◽  
Xiumei Jia
Keyword(s):  
Asymptotic Behavior ◽  
Hilbert Spaces ◽  
Measure Of Noncompactness ◽  
Infinite Delay ◽  
Mild Solutions ◽  
Sufficient Conditions ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Lipschitz Continuous ◽  
Stochastic Functional

In this paper, the existence and asymptotic stability in p-th moment of mild solutions to a class of second-order impulsive partial stochastic functional neutral integrodifferential equations with infinite delay in Hilbert spaces is considered. By using H?lder?s inequality, stochastic analysis, fixed point strategy and the theory of strongly continuous cosine families with the Hausdorff measure of noncompactness, a new set of sufficient conditions is formulated which guarantees the asymptotic behavior of the nonlinear second-order stochastic system. These conditions do not require the nonlinear terms are assumed to be Lipschitz continuous. An example is also discussed to illustrate the efficiency of the obtained results.

scholarly journals Stability and Boundedness of Solutions to Nonautonomous Parabolic Integrodifferential Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Michael Gil'
Keyword(s):  
Tensor Product ◽  
Hilbert Spaces ◽  
Integrodifferential Equations ◽  
Stability Of Solutions ◽  
Boundedness Of Solutions ◽  
Norm Estimates ◽  
Operator Functions

We consider a class of linear nonautonomous parabolic integrodifferential equations. We will assume that the coefficients are slowly varying in time. Conditions for the boundedness and stability of solutions to the considered equations are suggested. Our results are based on a combined usage of the recent norm estimates for operator functions and theory of equations on the tensor product of Hilbert spaces.

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