The Cauchy problem for certain generalized differential equations of second order

• Autorzy: Poreda T. , Szadkowska A.
• Języki publikacji: EN

Abstrakty

EN

The present paper concerns some generalized differential equations of second order for mappings from a subset of Banach space into a Banach space. The subject matter refers to studies of generalized differential equations of the first order submitted in [4]. Let X,Y be Banach spaces over the field R and let U, V be open subsets of X and V, respectively. Let h1, h2 be mappings from U into X. In this paper we study the Cauchy problem D2f(x)(h2(x)) = F{x, Df(x)(h1(x))), x € U for mappings from a subset of a Banach space into a Banach space, which are defined in C class, at a neighbourhood of nonsingular point (that is, at a neighbourhood of such point xo for whichh1(xo)= 0 and h2(xo= 0).

Słowa kluczowe

EN

Cauchy problem; Banach space; differential equations; Frobenius theorem

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 4
• Strony: 773--782
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Poreda T.

• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland

autor

Szadkowska A.

• Institute of Mathematics, Technical University of Łódź, Al. Politechniki 11, 90-924 Łódź, Poland

Bibliografia

• [1] R. Courant, D. Hilbert, Methods of Mathematical Physics, New York, London 1962.
• [2] J. Dieudonné, Foundations of Modern Analysis, New York 1960.
• [3] K. Maurin, Analysis p. I, PWN, Warsaw 1976.
• [4] T. Poreda, On generalized differential equations in Banach spaces, Dissertationes Math. 1991.
• [5] L. Schwartz, Analysé mathématique, p. I, Paris 1967.
• [6] Z. Semadeni, Banach Spaces of Continuous Functions, PWN, Warsaw 1971.
• [7] E. T. Whittaker, G. N. Watson, Modern analysis, London 1927.