An abstracts second order Cauchy problem with non-densely defined operator, II

• Autorzy: Bochenek J.
• Języki publikacji: EN

Abstrakty

EN

By using the theory of the extrapolation space X-1 associated with an operator A which is non-densely denned in a Banach space X, the existence and uniqueness of solutions of the semilinear second order differential initial value problem (1) is proved.

Słowa kluczowe

EN

value problem; extrapolation space

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 2
• Strony: 293--302
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Bochenek J.

• Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Krakow, Poland

Bibliografia

• [1] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Polon. Math. 54 (1991), 155-166.
• [2] J. Bochenek, An abstract second order Cauchy problem with non-densely defined operator, I, Demonstratio Math. 33 (2000), 489-501.
• [3] G. Da Prato, P. Grisvard, Maximal regularity for evolution equations by interpolation and extrapolation, J. Func. Anal. 58 (1984), 285-344.
• [4] H. O. Fattorini, Second order linear differential equations in Banach spaces, North-Holland, New York, 1985.
• [5] R. Nagel, Sobolev spaces and semigroups, Semesterberichte Funktionalanalysis 4 (1983), 1-20.
• [6] J. van Neerven, The adjoint of a semigroup of linear operators LNM 1529, Springer-Verlag, 1992.
• [7] 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.