Some existence results for solutions of differential inclusions with retardations

L. H. Erbe; W. Krawcewicz; Shaozhu Chen

Annales Polonici Mathematici (1991)

  • Volume: 54, Issue: 3, page 227-239
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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L. H. Erbe, W. Krawcewicz, and Shaozhu Chen. "Some existence results for solutions of differential inclusions with retardations." Annales Polonici Mathematici 54.3 (1991): 227-239. <http://eudml.org/doc/262514>.

@article{L1991,
abstract = {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.},
author = {L. H. Erbe, W. Krawcewicz, Shaozhu Chen},
journal = {Annales Polonici Mathematici},
keywords = {boundary value problem; differential inclusion with retardations; topological transversality; retarded differential inclusions; Carathéodory multifunction; topological transversality method; a priori bounds technique},
language = {eng},
number = {3},
pages = {227-239},
title = {Some existence results for solutions of differential inclusions with retardations},
url = {http://eudml.org/doc/262514},
volume = {54},
year = {1991},
}

TY - JOUR
AU - L. H. Erbe
AU - W. Krawcewicz
AU - Shaozhu Chen
TI - Some existence results for solutions of differential inclusions with retardations
JO - Annales Polonici Mathematici
PY - 1991
VL - 54
IS - 3
SP - 227
EP - 239
AB - 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.
LA - eng
KW - boundary value problem; differential inclusion with retardations; topological transversality; retarded differential inclusions; Carathéodory multifunction; topological transversality method; a priori bounds technique
UR - http://eudml.org/doc/262514
ER -

References

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  1. [1] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, 1977. 
  2. [2] K. C. Chang, The obstacle problems and partial differential equations with discontinuous nonlinearities, Comm. Pure Appl. Math. 33 (1980), 117-146. Zbl0405.35074
  3. [3] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, PWN, Warszawa 1982. 
  4. [4] J. Duvallet, A theorem of existence for discontinuous differential systems with two point boundary conditions, Nonlinear Anal. 13 (1989), 43-51. 
  5. [5] L. H. Erbe and W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y'), this issue, 195-226. Zbl0731.34078
  6. [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. Zbl0635.34016
  7. [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. [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. Zbl0092.32302
  9. [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. [10] A. Granas, R. Guenther and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1981). 
  11. [11] A. Granas, R. Guenther and J. W. Lee, On a theorem of S. Bernstein, Pacific J. Math. 74 (1978), 78-82. 
  12. [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. Zbl0476.34017
  13. [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. Zbl0539.34031
  14. [14] P. Hartman, Ordinary Differential Equations, Wiley, New York 1964. Zbl0125.32102
  15. [15] T. Kaczyński, Topological transversality and nonlinear equations in locally convex spaces, preprint, 1987. 
  16. [16] W. Krawcewicz, Contribution à la théorie des équations non linéaires dans les espaces de Banach, Dissertationes Math. 273 (1988). Zbl0677.47038
  17. [17] T. Pruszko, Topological degree methods in multivalued boundary value problems, Nonlinear Anal. 5 (9) (1981), 953-973. 
  18. [18] T. Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. 229 (1984). Zbl0543.34008
  19. [19] C. A. Stuart, Differential equations with discontinuous nonlinearities, Arch. Rational Mech. Anal. 63 (1976), 59-75. Zbl0393.34010

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