Browsing by Subject "mild solution"

Now showing 1 - 5 of 5

Access status: Open Access ,
Controllability of semilinear systems with fixed delay in control
(2015) Kumar, Surendra; Sukavanam, N.
In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assumptions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.
Access status: Open Access ,
Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
(2014) Arjunan, M. Mallika; Nadaf, N. Y.
In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
Access status: Open Access ,
Fractional evolution equation nonlocal problems with noncompact semigroups
(2016) Zhang, Xuping; Chen, Pengyu
This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.
Access status: Open Access ,
On an evolution inclusion in non-separable Banach spaces
(2009) Cernea, Aurelian
We consider a Cauchy problem for a class of nonconvex evolution inclusions in non-separable Banach spaces under Filippov-type assumptions. We prove the existence of solutions.
Access status: Open Access ,
On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces
(2011) Yang, YanLong; Wang, JinRong
In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.