Second order semilinear Volterra integrodifferential equation in Banach space

• Autorzy: Jan Bochenek
• Języki publikacji: EN

Abstrakty

EN

By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of some semilinear second order Volterra integrodifferential equations in Banach spaces is proved. The results are applied to some integro-partial differential equations.

Słowa kluczowe

EN

cosine family; semilinear Volterra equation

Kategorie tematyczne

• 34K05: General theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 3
• Strony: 231-241

Daty

wydano

1992

otrzymano

1991-06-05

poprawiono

1992-02-15

Twórcy

autor

Jan Bochenek

• Institute of Mathematics, Technical University of Cracow, Warszawska 24, 31-155 Kraków Poland

Bibliografia

• [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166.
• [2] H. O. Fattorini, Ordinary differential equation in linear topological spaces, I, J. Differential Equations 5 (1968), 72-105.
• [3] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966.
• [4] C. Travis and G. Webb, An abstract second order semilinear Volterra integrodifferential equation, SIAM J. Math. Anal. 10 (1979), 412-424.
• [5] C. Travis and G. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96.