On extremal solutions of differential equations with advanced argument

• Autorzy: Augustynowicz A. , Jankowski J.
• Języki publikacji: EN

Abstrakty

EN

We obtain existence of absolutely continuous extremal solutions of the problem u'(x) = F(x, u(x), u(h(x))), u(0) = u0, and the Darboux problem for u_xy(x, y) = G(x, y, u(x, y), u(H(x, y))), where h and H are arbitrary continuous deviated arguments.

Słowa kluczowe

EN

functional differential equations; advanced argument; extremal solutions; Darboux problem; Carathéodory condition

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
• Rocznik: 2006
• Tom: Vol. 46, [Z] 1
• Strony: 17--24
• Opis fizyczny: bibliogr. 6 poz.

Twórcy

autor

Augustynowicz A.

autor

Jankowski J.

• University of Gdansk Wita Stwosza 57, 80-952 Gdansk, Poland,

Bibliografia

• [1] A. Alexiewicz, W. Orlicz, Some remarks on the existence and uniqueness of solutions of the hyperbolic equation, Studia Mathematica 15 (1956), 201-215.
• [2] A. Augustynowicz, H. Leszczyński, W. Walter, On some nonlinear ordinary differential equations with advanced arguments, Nonlinear Analysis 53 (2003), 495-505.
• [3] B. C. Dhage, On existence of extremal solutions of nonlinear functional integral equations in Banach algebras, Journal of Applied Mathematics and Stochastic Analysis 3 (2004), 271-282.
• [4] G. Herzog, R. Lemmert, On maximal and minimal solutions for x0(t) = F(t, x(t), x(h(t))), x(0) = x0, Annales Societatis Mathematicae Polonae, Series I: Commentationes Mathematicae XL (2000), 93-102.
• [5] W. Walter, Ordinary Differential Equations, Graduate Texts in Mathematics, Springer-Verlag New York 1998.
• [6] W. Walter, Differential and Integral Inequalities, Springer-Verlag, Berlin 1970.