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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.

Non-Leibniz algebras with logarithms do not have the trigonometric identity

D. Przeworska-Rolewicz (2000)

Banach Center Publications

Let X be a Leibniz algebra with unit e, i.e. an algebra with a right invertible linear operator D satisfying the Leibniz condition: D(xy) = xDy + (Dx)y for x,y belonging to the domain of D. If logarithmic mappings exist in X, then cosine and sine elements C(x) and S(x) defined by means of antilogarithmic mappings satisfy the Trigonometric Identity, i.e. [ C ( x ) ] 2 + [ S ( x ) ] 2 = e whenever x belongs to the domain of these mappings. The following question arises: Do there exist non-Leibniz algebras with logarithms such that...

Nonlinear mixed Volterra-Fredholm integrodifferential equation with nonlocal condition

Haribhau L. Tidke, Machindra B. Dhakne (2012)

Applications of Mathematics

The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.

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