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Abstrakty
Sufficient conditions for the uniqueness, global existence and for the convergence to zero when t -> oo of solutions of an integral equation related to an epidemic model are proved. The existence result is proved by applying the Banach fixed point theorem and for the proof of the convergence result a new type of integral inequality is used.
Wydawca
Czasopismo
Rocznik
Tom
Strony
603--609
Opis fizyczny
Bibliogr. 10 poz.
Twórcy
autor
- Department of Information Systems, Faculty of Management, Comenius University, Odbojarov Str. 10, 831 04 Bratislava, Slovakia
Bibliografia
- [1] J. A. Bihari, A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Sci. Hungar. 7 (1965), 81-94.
- [2] L. Górniewicz, R. S. Ingarden, Algebra z Geometria dla Fizyków 2, Univ. M. Kopernika, Toruń, 2000 (in Polish).
- [3] G. Gripenberg, On some epidemic models, Quart. Appl. Math. 39 (1981), 317-327.
- [4] A. A. Martyniuk, V. Lakshmikanthan, S. Leela, Motion Stability: The Method of Integral Inequalities, Naukova Dumka, Kiev, 1977.
- [5] M. Medved, A new approach to an analysis of Henry type integral inequalities and their Bihari type versions, J. Math. Anal. Appl. 214 (1997), 349-366.
- [6] M. Medved, Singular integral inequalities and stability of semilinear parabolic equations, Arch. Math. (Brno) 34, 1 (1998), 183-190.
- [7] M. Medved, Nonlinear singular difference inequalities suitable for discretizations of parabolic equations, Demonstratio Math. 33, 3 (2000), 517-525.
- [8] M. Medved, Nonlinear singular inequalities for functions in two and n independent variables, J. Inequal. Appl. 5 (2000), 1-22.
- [9] M. Medved, Integral inequalities and global solutions of semilinear evolution equations, J. Math. Anal. Appl. 267 (2002), 643-650.
- [10] B. G. Pachpatte, On a new inequality suggested by the study of certain epidemic models, J. Math. Anal, and Appl 195 (1995), 638-644.
Typ dokumentu
Bibliografia
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bwmeta1.element.baztech-article-PWA3-0007-0015