Stanĕk, Svatoslav Multiple solutions for some functional boundary value problems. (English) Zbl 0945.34049 Nonlinear Anal., Theory Methods Appl. 32, No. 3, 427-438 (1998). Second-order functional-differential equations are considered. The existence of at least two different solutions to the boundary value problem for this equation is proved. Sufficient conditions for the existence are given. Reviewer: Angela Slavova (Sofia) Cited in 5 Documents MSC: 34K10 Boundary value problems for functional-differential equations 34K12 Growth, boundedness, comparison of solutions to functional-differential equations Keywords:functional-differential equations; boundary value problem PDFBibTeX XMLCite \textit{S. Stanĕk}, Nonlinear Anal., Theory Methods Appl. 32, No. 3, 427--438 (1998; Zbl 0945.34049) Full Text: DOI References: [1] Brykalov, S. A., A second-order nonlinear problem with two-point and integral boundary conditions, (Proceeding Georgian Acad. Sci. Math., 1 (1993)), 273-279, (3) · Zbl 0798.34021 [2] Brykalov, S. A., Solvability of a nonlinear boundary value problem in a fixed set of functions, Diff. Urav., 27, 12, 2027-2033 (1991), (In Russian) · Zbl 0743.34070 [3] Deimling, K., Nonlinear Functional Analysis (1985), Springer-Verlag: Springer-Verlag Berlin · Zbl 0559.47040 [4] Fabry, C.; Mawhin, J.; Nkashama, M. N., A multiplicity results for periodic solutions of forced nonlinear second order ordinary differential equations, Bull. London Math. Soc., 18, 173-180 (1986) · Zbl 0586.34038 [5] Nkashama, M. N.; Santanilla, J., Existence of multiple solutions for some nonlinear boundary value problems, J. Differential Equations, 84, 148-164 (1990) · Zbl 0693.34011 [6] Staněk, S., Existence of multiple solutions for some functional boundary value problems, Arch. Math. (Brno), 28, 57-65 (1992) · Zbl 0782.34074 [7] Staněk, S., Multiplicity results for second order nonlinear problems with maximum and minimum. (To Appear in Math. Nochr.; Staněk, S., Multiplicity results for second order nonlinear problems with maximum and minimum. (To Appear in Math. Nochr. [8] Šeda, V., Fredholm mappings and the generalized boundary value problem, Differential and Integral Equations, 8, 19-40 (1995) · Zbl 0818.34014 [9] Bihari, I., A generalization of a lemma of Bellman and its application to uniqueness problems of differential equations, Acta Math. Acad. Sci. Hung., 7, 71-94 (1956) · Zbl 0070.08201 [10] Filatov, A. N.; Sharova, L. V., Integral Inequalities and Theory of Nonlinear Oscillations (1976), Nauka: Nauka Moscow, (In Russian.) · Zbl 0463.34001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.