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Boundary value problems for nonlinear ordinary differential equations of second order in Banach spaces. (English) Zbl 0462.34041

MSC:
34G20Nonlinear ODE in abstract spaces
34A34Nonlinear ODE and systems, general
34B15Nonlinear boundary value problems for ODE
34A12Initial value problems for ODE, existence, uniqueness, etc. of solutions
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Full Text: DOI
References:
[1] Chandra, J.; Lakshmikantham, V.; Mitchell, A. R.: Existence of solutions of boundary value problems for nonlinear second order systems in a Banach space. Nonlinear analysis 2, 157-168 (1978) · Zbl 0385.34035
[2] Daher, J.: On a fixed point principle of sadovskii. Nonlinear analysis 2, 643-645 (1978) · Zbl 0377.47038
[3] Deimling, K.: Ordinary differential equations in Banach spaces. Lecture notes 596 (1977) · Zbl 0361.34050
[4] Deimling, K.: Periodic solutions of differential equations in Banach spaces. Man. math. 24, 31-44 (1978) · Zbl 0373.34032
[5] Diestel, J.: Geometry of Banach spaces--selected topics. Lecture notes 485 (1975) · Zbl 0307.46009
[6] Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations. Lecture notes 568 (1977) · Zbl 0339.47031
[7] Kuratowski, C.: Sur LES espaces complets. Fundam. math. 15, 301-309 (1930) · Zbl 56.1124.04
[8] Lemmert, R.; Volkmann, P.: Randwertprobleme für gewöhnliche differentialgleichungen in konvexen teilmengen eines banachraumes. J. diff. Eqns. 27, 138-143 (1978) · Zbl 0388.34038
[9] Mönch, H.: Existenz für Sturm-Liouville-probleme. Dissertation Paderborn (1979)
[10] Sadovskii, B. N.: Limit-compact and condensing operators. Russ. math. Survs. 27, 85-155 (1972) · Zbl 0243.47033
[11] Schmitt, K.; Thompson, R. C.: Boundary value problems for infinite systems of second order differential equations. J. diff. Eqns. 18, 277-295 (1975) · Zbl 0302.34081
[12] Schmitt, K.; Volkmann, P.: Boundary value problems for second order differential equations in convex subsets in a Banach space. Trans. am. Math. soc. 218, 397-405 (1976) · Zbl 0334.34054
[13] Schröder, J.: Inverse-monotone nonlinear differential operators of the second order. Proc. R. Soc. edinb. 79A, 193-216 (1977) · Zbl 0412.34008