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Abstrakty
A theorem about a system of weak implicit impulsive nonlinear parabolic functional-differential inequalities in an arbitrary parabolic set is proved. As a consequence of the theorem, maximum principles for the system of implicit impulsive nonlinear parabolic functional-differential inequalities and the uniqueness of a classical solution of a mixed implicit impulsive problem for a system of nonlinear parabolic functional-differential equations are obtained.
Czasopismo
Rocznik
Tom
Strony
5--18
Opis fizyczny
Bibliogr. 11 poz.
Twórcy
autor
- Institute of Mathematics, Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland, lbyszews@usk.pk.edu.pl
Bibliografia
- [1] BAINOV D., KAMONT Z., MINCHEV E., Initial - boundary value problems for impulsive parabolic functional - differential equations, Applicationes Math-ematicae, 24(1)(1996), 1-15.
- [2] BESALA P., An extension of the strong maximum principle for parabolic equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 19(1971), 1003-1006.
- [3] BVSZEWSKI L., Strong maximum principle for implicit non-linear parabolic functional-differential inequalities in arbitrary domains, Univ. lagell. Acta Math., 24(1984), 327-339.
- [4] BYSZEWSKI L., Impulsive implict weak nonlinear parabolic functional - differential inequalities, Journal Math. Phys. Sci., 26(6)(1992), 513-527.
- [5] BYSZEWSKI L., A system of impulsive nonlinear parabolic functional -differential inequalities, Comment. Math., 35 (1995), 83-95.
- [6] LAKSHMIKANTHAM V., BAINOV D., SIMEONOV P., Theory of Impulsive Differential Equations, World Scientific, Singapore 1989.
- [7] REDHEFFER R., WALTER W., Das Maximumprinzip in unbeschrankten Gebieten fur parabolische Ungleichungen mit Funktionalen, Math. Ann., 226(1977), 155-170.
- [8] SZARSKI J., Differential Inequalities, PWN, Warszawa 1967.
- [9] SZARSKI J., Strong maximum principle for non-linear parabolic differential - functional inequalities in arbitrary domains, Ann. Polon. Math., 29(1974), 207-217.
- [10] WALTER W., Differential and Integral Inequalities, Springer - Verlag, Berlin, Heidelberg, New York 1970.
- [11] YOSHIDA N., Maximum principles for implicit parabolic equations, Proc. Japan Acad., (1973), 785-788.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPP1-0069-0077