Uniqueness of solutions of a generalized Cauchy problem for a system of first order partial functional differential equations

• Autorzy: Netka M.
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with weak solutions of a generalized Cauchy problem for a nonlinear system of first order differential functional equations. A theorem on the uniqueness of a solution is proved. Nonlinear estimates of the Perron type are assumed. A method of integral functional inequalities is used.

Słowa kluczowe

EN

functional differential equations; comparison methods; nonlinear estimates of Perron type

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2009
• Tom: Vol. 29, no. 1
• Strony: 69--79
• Opis fizyczny: Bibliogr. 6 poz.

Twórcy

autor

Netka M.

• University of Gdańsk, Institute of Mathematics, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland,

Bibliografia

• [1] V. Lakshmikantham, S. Koksal, Monotone Flows and Rapid Convergence for Nonlinear Partial Differential Equations, Taylor & Francis, London, 2003.
• [2] V. Lakshmikantham, S. Leela, Differential and Integral Inequalities: Theory and Applications, Academic Press, New York, 1996.
• [3] Z. Kamont, Hyperbolic Functional Differential Inequalities and Applications, Kluwer Academic Publishers, Dordrecht, 1999.
• [4] Z. Kamont, A. Salvadori, Uniqueness of solutions to hyperbolic functional-differential problems, Nonlinear Anal. 30 (1997), 4585-4594.
• [5] J. Szarski, Differential Inequalities, Państwowe Wydawnictwo Naukowe, Warsaw, 1965.
• [6] J. Szarski, Generalized Cauchy problem for differential-functional equations with first order partial derivatives, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 24 (1976), 575-580.