Staněk, Svatoslav Leray-Schauder degree method in functional boundary value problems depending on the parameter. (English) Zbl 0805.34053 Math. Nachr. 164, 333-344 (1993). Summary: Using the Leray-Schauder degree method sufficient conditions for the one- parameter boundary value problem \(x'' = f(t,x,x', \lambda)\), \(\alpha (x) = A\), \(x(0) - x(1) = B\), \(x'(0) - x'(1)=C\), are stated. The application is given for a class of functional boundary value problems for nonlinear third-order functional differential equations depending on the parameter. Cited in 4 Documents MSC: 34K10 Boundary value problems for functional-differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:Leray-Schauder degree method; one-parameter boundary value problem; functional boundary value problems; nonlinear third-order functional differential equations × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Arscott, Proc. London Math. Soc. (3) 14 pp 459– (1964) [2] Nonlinear Functional Analysis. Springer-Verlag, Berlin, Heidelberg, 1985 · doi:10.1007/978-3-662-00547-7 [3] and , Nonlinear Boundary Value Problems for Ordinary Differential Equations. Dissertationes Mathematicae (Rozprawy Mat.) CCXLIV, Warszawa, 1985 [4] Greguš, J. London Math. Soc. (2) 3 pp 429– (1971) [5] On a certain boundary value problem for third order differential equation. An. st. Univ. Iasi, XXXII, f. 1, s. Ia, Mat. (1986), 55–61 [6] Stanêk, Czech. Math. J. 42 pp 241– (1992) [7] Stanêk, Czech. Math. J. 42 pp 257– (1992) [8] Stanêk, Math. Slovaca 42 pp 85– (1992) [9] Stanêk, Acta UPO, Fac. rer. nat. 97, Math. pp 107– (1990) [10] On a class of five-point boundary value problems for nonlinear second-order differential equations depending on the parameter. Acta Math. Hungar. (in press) [11] On a class of functional boundary value problems for second-order functional differential equations with parameter. Czech. Math. J. (in press) [12] On certain three-point regular boundary value problems for nonlinear second-order differential equations depending on the parameter (1992), submitted for publication [13] Stanêk, Acta UPO, Fac. rer. nat. 100, Math. pp 61– (1991) [14] On a class of functional boundary value problems for nonlinear third-order functional differential equations depending on the parameter (1992), submitted for publication 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.