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.
@article{bwmeta1.element.bwnjournal-article-apmv54z3p227bwm,
author = {L. H. Erbe and W. Krawcewicz and Shaozhu Chen},
title = {Some existence results for solutions of differential inclusions with retardations},
journal = {Annales Polonici Mathematici},
volume = {55},
year = {1991},
pages = {227-239},
zbl = {0731.34079},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p227bwm}
}
L. H. Erbe; W. Krawcewicz; Shaozhu Chen. Some existence results for solutions of differential inclusions with retardations. Annales Polonici Mathematici, Tome 55 (1991) pp. 227-239. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv54z3p227bwm/
[000] [1] C. Castaing and M. Valadier, Convex Analysis and Measurable Multifunctions, Lecture Notes in Math. 580, Springer, 1977.
[001] [2] K. C. Chang, The obstacle problems and partial differential equations with discontinuous nonlinearities, Comm. Pure Appl. Math. 33 (1980), 117-146. | Zbl 0405.35074
[002] [3] J. Dugundji and A. Granas, Fixed Point Theory, Vol. 1, PWN, Warszawa 1982.
[003] [4] J. Duvallet, A theorem of existence for discontinuous differential systems with two point boundary conditions, Nonlinear Anal. 13 (1989), 43-51.
[004] [5] L. H. Erbe and W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y'' ∈ F(t,y,y'), this issue, 195-226. | Zbl 0731.34078
[005] [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. | Zbl 0635.34016
[006] [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).
[007] [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. | Zbl 0092.32302
[008] [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.
[009] [10] A. Granas, R. Guenther and J. W. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1981).
[010] [11] A. Granas, R. Guenther and J. W. Lee, On a theorem of S. Bernstein, Pacific J. Math. 74 (1978), 78-82.
[011] [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. | Zbl 0476.34017
[012] [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. | Zbl 0539.34031
[013] [14] P. Hartman, Ordinary Differential Equations, Wiley, New York 1964. | Zbl 0125.32102
[014] [15] T. Kaczyński, Topological transversality and nonlinear equations in locally convex spaces, preprint, 1987.
[015] [16] W. Krawcewicz, Contribution à la théorie des équations non linéaires dans les espaces de Banach, Dissertationes Math. 273 (1988). | Zbl 0677.47038
[016] [17] T. Pruszko, Topological degree methods in multivalued boundary value problems, Nonlinear Anal. 5 (9) (1981), 953-973.
[017] [18] T. Pruszko, Some applications of the topological degree theory to multivalued boundary value problems, Dissertationes Math. 229 (1984). | Zbl 0543.34008
[018] [19] C. A. Stuart, Differential equations with discontinuous nonlinearities, Arch. Rational Mech. Anal. 63 (1976), 59-75. | Zbl 0393.34010