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Empathy theory and the Laplace transform

Niko Sauer (1997)

Banach Center Publications

This paper is concerned with double families of evolution operators employed in the study of dynamical systems in which cause and effect are represented in different Banach spaces. The main tool is the Laplace transform of vector-valued functions. It is used to define the generator of the double family which is a pair of unbounded linear operators and relates to implicit evolution equations in a direct manner. The characterization of generators for a special class of evolutions is presented.

Équations différentielles algébriques

Jean-Louis Verdier (1977/1978)

Séminaire Bourbaki

Équations différentielles linéaires et majorations de multiplicités

Daniel Bertrand, Frits Beukers (1985)

Annales scientifiques de l'École Normale Supérieure

Evolution operators for higher order abstract parabolic equations

Enrico Obrecht (1986)

Czechoslovak Mathematical Journal

Evolution operators related to semi-groups of class (A).

N. Sauer, J.E. Singleton (1986/1987)

Semigroup forum

Exact controllability of a non-linear generalized damped wave equation: Application to the sine-Gordon equation.

Leiva, Hugo (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Exact linear lumping in abstract spaces.

Rózsa, Zoltán, Tóth, János (2003)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence and regularity results for abstract non autonomous parabolic equations

Paolo Acquistapace, Brunello Terreni (1982)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Si studiano esistenza, unicità e regolarità delle soluzioni strette, classiche e forti dell’equazione di evoluzione non autonoma $u^{\prime}(t)—A(t)u(t)=f(t)$ , con il dato iniziale $u(0)=x$ , in spazi di Banach. I dominii degli operatori $A(t)$ variano in $t$ e non sono necessariamente densi in $E$ . Si danno condizioni necessarie e sufficienti per l'esistenza e la regolarità holderiana della soluzione e della sua derivata.

Existence and uniqueness of periodic solutions of linear differential equations in Banach spaces

Ivan Straškraba (1982)

Czechoslovak Mathematical Journal

Existence of convex and non convex local solutions for fractional differential inclusions.

Ibrahim, Rabha W. (2009)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of solutions for integrodifferential inclusions in Banach spaces.

Papageorgiou, Nikolaos S. (1991)

Commentationes Mathematicae Universitatis Carolinae

Existence of the fundamental solution of a second order evolution equation

Jan Bochenek (1997)

Annales Polonici Mathematici

We give sufficient conditions for the existence of the fundamental solution of a second order evolution equation. The proof is based on stable approximations of an operator A(t) by a sequence $A_{n} (t)$ of bounded operators.

Existence of weak solutions for abstract hyperbolic-parabolic equations.

Clark, Marcondes Rodrigues (1994)

International Journal of Mathematics and Mathematical Sciences

Existence results for a second-order abstract Cauchy problem with nonlocal conditions.

Hernández M., Eduardo, Pelicer, Mauricio L. (2005)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence results for differential equations in Banach spaces

John W. Lee, Donal O'Regan (1993)

Commentationes Mathematicae Universitatis Carolinae

This paper presents existence results for initial and boundary value problems for nonlinear differential equations in Banach spaces.

Existence theorems for differential inclusions with nonconvex right-hand side.

Papageorgiou, Nikolaos S. (1986)

International Journal of Mathematics and Mathematical Sciences

Existence, uniqueness and continuous dependence of solutions of differential equations in Banach space

Michał Kisielewicz (1989)

Annales Polonici Mathematici

Explicit solutions for boundary value problems related to the operator equations $X^{(2)} - A X = 0$

Lucas Jódar, Enrique A. Navarro (1991)

Applications of Mathematics

Cauchy problem, boundary value problems with a boundary value condition and Sturm-Liouville problems related to the operator differential equation $X^{(2)} - A X = 0$ are studied for the general case, even when the algebraic equation $X^{2} - A = 0$ is unsolvable. Explicit expressions for the solutions in terms of data problem are given and computable expressions of the solutions for the finite-dimensional case are made available.

Exponential dichotomy for evolution families on the real line.

Sasu, Adina Luminiţa (2006)

Abstract and Applied Analysis

Exponential dichotomy of evolutionary processes in Banach spaces

Petre Preda, Mihail Megan (1985)

Czechoslovak Mathematical Journal

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