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Abstrakty
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.
Wydawca
Rocznik
Tom
Strony
17--24
Opis fizyczny
bibliogr. 6 poz.
Twórcy
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.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUS5-0004-0015