An abstract nonlinear second order differential equation

• 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 a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.

Kategorie tematyczne

• 34K30: Equations in abstract spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 54
• Numer: 2
• Strony: 155-166

Daty

wydano

1991

otrzymano

1989-12-06

poprawiono

1990-06-11

Twórcy

autor

Jan Bochenek

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

Bibliografia

• [1] T. Kato, Perturbation Theory for Linear Operators, Springer, 1966.
• [2] R. Rabczuk, Elements of the Theory of Differential Inequalities, PWN, Warszawa 1976 (in Polish).
• [3] I. Segal, Nonlinear semi-groups, Ann. of Math. 78 (1963), 339-364.
• [4] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungar. 32 (1978), 75-96.
• [5] T. Winiarska, Differential Equations with Parameter, Monograph 68, Technical University of Cracow, 1988.
• [6] K. Yosida, Functional Analysis, Springer, New York 1980.