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Near viability for fully nonlinear differential inclusions

Irina Căpraru, Alina Lazu (2014)

Open Mathematics

We consider the nonlinear differential inclusion x′(t) ∈ Ax(t) + F(x(t)), where A is an m-dissipative operator on a separable Banach space X and F is a multi-function. We establish a viability result under Lipschitz hypothesis on F, that consists in proving the existence of solutions of the differential inclusion above, starting from a given set, which remain arbitrarily close to that set, if a tangency condition holds. To this end, we establish a kind of set-valued Gronwall’s lemma and a compactness...

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.

New spectral criteria for almost periodic solutions of evolution equations

Toshiki Naito, Nguyen Van Minh, Jong Son Shin (2001)

Studia Mathematica

We present a general spectral decomposition technique for bounded solutions to inhomogeneous linear periodic evolution equations of the form ẋ = A(t)x + f(t) (*), with f having precompact range, which is then applied to find new spectral criteria for the existence of almost periodic solutions with specific spectral properties in the resonant case where e i s p ( f ) ¯ may intersect the spectrum of the monodromy operator P of (*) (here sp(f) denotes the Carleman spectrum of f). We show that if (*) has a bounded...

Nonlinear evolution inclusions arising from phase change models

Pierluigi Colli, Pavel Krejčí, Elisabetta Rocca, Jürgen Sprekels (2007)

Czechoslovak Mathematical Journal

The paper is devoted to the analysis of an abstract evolution inclusion with a non-invertible operator, motivated by problems arising in nonlocal phase separation modeling. Existence, uniqueness, and long-time behaviour of the solution to the related Cauchy problem are discussed in detail.

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