Abstract
This chapter presents general principles that can be used to establish existence to particular boundary value problems. The existence principles that follow are formulated for 2nd order systems. Corresponding principles for systems of other orders will be clear from the discussion that follows. Moreover, except for some minor notational changes, the proofs of the more general results are the same as for the 2nd order case. The results presented here are based on ideas presented by Granas, Guenther and Lee [7] in 1991.
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References
D.R. Dunninger and J.C. Kurtz, Existence of solutions for some nonlinear singular boundary value problems, J. Math. Anal. Appl., 115 (1986), 396 – 405.
M. Frigon, Application de la théorie de la transversalité topologies a des problémes nonlinéaires pour des équations différentielles ordinaires, Diss. Math., 296 (1990), 1 – 79.
M. Frigon and D. O’Regan, On a generalisation of a theorem of S. Bernstein, Ann. Polon. Math., 48 (1988), 297 – 306.
R.E. Gaines and J. Mawhin, Coincidence degree and nonlinear differential equations, Springer Lecture notes, 567, New York, 1977.
A. Granas and Z. Guennoun, Quelques résultats dans la théorie de Bernstein Carathéodory de l’équation y" = f (t, y, y’), C. R. Acad. Sci. Paris, 306 (1988), 703 - 706.
A. Granas, R.B. Guenther and J.W. Lee, Nonlinear boundary value problems for ordinary differential equations, Diss. Math., 244, Warsaw, 1985.
A. Granas, R.B. Guenther and J.W. Lee, Some general existence principles in the Carathéodory theory of nonlinear differential systems, J. Math. Pures et Appl., 70 (1991), 153 – 196.
J.W. Lee and D. O’Regan, Existence principles for differential equations and systems of equations, Topological methods in Diff. Eqns. and Inclusions (edited by A. Granas and M. Frigon ), NATO ASI Series C, Kluwer Acad. Publ., Dordrecht, 1995, 239 - 289.
J. Mawhin, Topolical degree methods in nonlinear boundary value problems, AMS Regional Conf. Series in Math., 40, Providence, 1979.
K. Schmidt and R. Thompson, Boundary value problems for infinite systems of second order differential equations, J. Diff. Eqns., 18 (1975), 277 – 295.
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© 1997 Springer Science+Business Media Dordrecht
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O’Regan, D. (1997). Existence principles for second order boundary value problems. In: Existence Theory for Nonlinear Ordinary Differential Equations. Mathematics and Its Applications, vol 398. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1517-1_5
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DOI: https://doi.org/10.1007/978-94-017-1517-1_5
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