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Integro-differential equations on time scales with Henstock-Kurzweil delta integrals

Aneta Sikorska-Nowak (2011)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper we prove existence theorems for integro - differential equations x Δ ( t ) = f ( t , x ( t ) , ∫ ₀ t k ( t , s , x ( s ) ) Δ s ) , t ∈ Iₐ = [0,a] ∩ T, a ∈ R₊, x(0) = x₀ where T denotes a time scale (nonempty closed subset of real numbers R), Iₐ is a time scale interval. Functions f,k are Carathéodory functions with values in a Banach space E and the integral is taken in the sense of Henstock-Kurzweil delta integral, which generalizes the Henstock-Kurzweil integral. Additionally, functions f and k satisfy some boundary conditions and conditions...

Local center manifold for parabolic equations with infinite delay

Hana Petzeltová (1994)

Mathematica Bohemica

The existence and attractivity of a local center manifold for fully nonlinear parabolic equation with infinite delay is proved with help of a solutions semigroup constructed on the space of initial conditions. The result is applied to the stability problem for a parabolic integrodifferential equation.

Maximal regularity of delay equations in Banach spaces

Carlos Lizama, Verónica Poblete (2006)

Studia Mathematica

We characterize existence and uniqueness of solutions for an inhomogeneous abstract delay equation in Hölder spaces. The main tool is the theory of operator-valued Fourier multipliers.

Maximal regularity of second-order evolution equations with infinite delay in Banach spaces

Xianlong Fu, Ming Li (2014)

Studia Mathematica

By using Fourier multiplier theorems we characterize the existence and uniqueness of periodic solutions for a class of second-order differential equations with infinite delay. We also establish maximal regularity results for the equations in various spaces. An example is provided to illustrate the applications of the results obtained.

Neutral functional differential and integrodifferential inclusions in Banach spaces

M. Benchohra, S. K. Ntouyas (2001)

Bollettino dell'Unione Matematica Italiana

In questo lavoro studiamo l'esistenza di soluzioni deboli su un intervallo compatto di problemi con valore iniziale per inclusioni funzionali neutre differenziali e integrodifferenziali in spazi di Banach. I risultati sono ottenuti usando un teorema di punto fisso per mappe condensanti dovuto a Martelli.

Neutral functional integrodifferential control systems in Banach spaces

Krishnan Balachandran, E. Radhakrishnan Anandhi (2003)

Kybernetika

Sufficient conditions for controllability of neutral functional integrodifferential systems in Banach spaces with initial condition in the phase space are established. The results are obtained by using the Schauder fixed point theorem. An example is provided to illustrate the theory.

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