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1991 | 54 | 3 | 227-239
Tytuł artykułu

Some existence results for solutions of differential inclusions with retardations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Using the topological transversality method of Granas we prove an existence result for a system of differential inclusions with retardations of the form y'' ∈ F(t,y,y',Φ(y)). The result is applied to the study of the existence of solutions to an equation of the trajectory of an r-stage rocket with retardations.
Rocznik
Tom
54
Numer
3
Strony
227-239
Opis fizyczny
Daty
wydano
1991
otrzymano
1988-11-02
poprawiono
1989-05-15
poprawiono
1990-01-15
Twórcy
autor
  • Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada
  • Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada
autor
  • Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada
Bibliografia
  • [1] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, 1977.
  • [2] K. C. Chang, The obstacle problems and partial differential equations with discontinuous nonlinearities, Comm. Pure Appl. Math. 33 (1980), 117-146.
  • [3] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, PWN, Warszawa 1982.
  • [4] J. Duvallet, A theorem of existence for discontinuous differential systems with two point boundary conditions, Nonlinear Anal. 13 (1989), 43-51.
  • [5] L. H. Erbe and W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y'), this issue, 195-226.
  • [6] L. H. Erbe and K. Schmitt, On solvability of boundary value problems for systems of differential equations, J. Appl. Math. Phys. 38 (1987), 184-192.
  • [7] M. Frigon, Application de la théorie de la transversalité topologique à des problèmes non linéaires pour certaines classes d'équations différentielles ordinaires, Dissertationes Math. 296 (1990).
  • [8] A. Granas, Homotopy extension theorem in Banach spaces and some of its applications to the theory of nonlinear equations, Bull. Acad. Polon. Sci. 7 (1959), 387-394.
  • [9] A. Granas et Zine el Abdine Guennoun, Quelques résultats dans la théorie de Bernstein-Carathéodory de l'équation y'' = f(t,y,y'), C. R. Acad. Sci. Paris Sér. I 306 (1988), 703-706.
  • [10] A. Granas, R. Guenther and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1981).
  • [11] A. Granas, R. Guenther and J. W. Lee, On a theorem of S. Bernstein, Pacific J. Math. 74 (1978), 78-82.
  • [12] A. Granas, R. Guenther and J. W. Lee, Nonlinear boundary value problems for some classes of ordinary differential equations, Rocky Mountain J. Math. 10 (1980), 35-58.
  • [13] J. Haddad and J. M. Lasry, Periodic solutions of functional differential inclusions and fixed points of G-selectionable correspondences, J. Math. Anal. Appl. 110 (1983), 295-312.
  • [14] P. Hartman, Ordinary Differential Equations, Wiley, New York 1964.
  • [15] T. Kaczyński, Topological transversality and nonlinear equations in locally convex spaces, preprint, 1987.
  • [16] W. Krawcewicz, Contribution à la théorie des équations non linéaires dans les espaces de Banach, Dissertationes Math. 273 (1988).
  • [17] T. Pruszko, Topological degree methods in multivalued boundary value problems, Nonlinear Anal. 5 (9) (1981), 953-973.
  • [18] T. Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. 229 (1984).
  • [19] C. A. Stuart, Differential equations with discontinuous nonlinearities, Arch. Rational Mech. Anal. 63 (1976), 59-75.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-apmv54z3p227bwm
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