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Local bounds and existence of solutions to non-convex differential inclusions

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Abstrakty
EN
Using a global bifurcation theorem for convex-valued completely continuous mapping we prove an existence theorem for differential inclusions of the form u" is an element of F(t,u,u'}, where F admits a convex-valued, weakly completely continuous selector and u satisfies some nonlinear boundary conditions.
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65--74
Opis fizyczny
Bibliogr. 18 poz.
Twórcy
Bibliografia
  • [1] H. A. Antosiewicz, A. Cellina, Continuous selectors and differential relations, J. Differential Equations 19 (1975), 386-398.
  • [2] A. Bressan, G. Colombo, Extensions and selections of maps decomposable values, Stud. Math. 90 (1988), 70-85.
  • [3] E. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
  • [4] S. Domachowski, J. Gulgowski, A global bifurcation theorem for convex-valued differential inclusions, Zeitschrift fur Analysis und ihre Anwendungen 23 (2004), 275-292.
  • [5] L. H. Erbe, W. Krawcewicz, Nonlinear boundary value problems for differential inclusions y" Є F(t, y, y'), Ann. Polon. Math. 54 (1991), 195-226.
  • [6] M. Frigon, A. Granas, Théoremes d’existence pour des inclusions différentiielles sans convexité, C.R. Acad. Sci. Paris, Serie I Math. 310 (1990), 819-822.
  • [7] A. Fryszkowski, Continuous selections for a class of non-convex multi-valued maps, Stud. Math. 76 (1983), 163-174.
  • [8] A. Granas, R. B. Guenther, J. W. Lee, On a theorem of S. Bernstein, Pacific Math. 73 (2) (1977), 67-82.
  • [9] A. Granas, R. B. Guenther, J. W. Lee, Nonlinear boundary value problems for some classes of ordinary differential equations, Dissertationes Math. 244 (1985).
  • [10] P. Hartman, Ordinary Differential Equations, Birkhauser, Boston-Basel-Stuttgart, 1982.
  • [11] S. Łojasiewicz (Jr), The existence of solutions for lower semicontinuous orientor fields, Bull. Acad. Polon. Sci. 9-10 (1980), 483-487.
  • [12] S. A. Mararano, Existence theorems for a multi-valued boundary value problem, Bull. Austral. Math. Soc. 45 (1992), 249-260.
  • [13] A. Pliś, Measurable orientor fields, Bull. Acad. Polon. Sci. 8 (1965), 857-859.
  • [14] M. H. Protter, H. F. Weinberger, Maximum Principles in Differential Equations, Springer-Verlag, New York, 1984.
  • [15] T. Pruszko, Topological degree methods in multi-valued boundary value problems, J. Nonlinear Anal. 9 (1981), 959-973.
  • [16] T. Pruszko, Some applications of the topological degree theory to multi-valued boundary value problems, Dissertationes Math. 229 (1984), 1-52.
  • [17] P. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. of Funct. Anal. 7 (1971), 487-513.
  • [18] O. N. Ricceri, B. Ricceri, An existence theorem for inclusions of the type Φ(u)(t) Є F(t,Φ(u)(t)) and application to a multi-valued boundary value problem, Appl. Anal. 38 (1990), 259-270.
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Bibliografia
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bwmeta1.element.baztech-article-PWA3-0051-0006
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