×

zbMATH — the first resource for mathematics

Existence theorems for a second order three-point boundary value problem. (English) Zbl 0879.34025
Summary: Existence results for the second-order three-point boundary value problem \(x''= f(t,x,x')\), \(x(0)=A\), \(x(\eta)- x(1)= (\eta-1)B\), \(0<\eta<1\), are presented. Our analysis is based on a nonlinear alternative of Leray-Schauder.

MSC:
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aftablzadeh, A.R.; Gupta, C.P.; Xu, Jian-Ming, Existence and uniqueness theorems for three-point boundary value problem, SIAM J. math. anal., 20, 716-726, (1989) · Zbl 0704.34019
[2] Berger, M.; Fraenkel, Nonlinear desingularization in certain free-boundary problems, Comm. math. phys., 77, 149-172, (1980) · Zbl 0454.35087
[3] Boucherif, A., Nonlinear three-point boundary value problems, J. math. anal. appl., 77, 577-600, (1980) · Zbl 0444.34024
[4] Boucherif, A., Nonlinear multipoint boundary value problems, Nonlinear anal., 10, 957-964, (1986) · Zbl 0607.34014
[5] Granas, A.; Guenther, R.B.; Lee, J.W., Nonlinear boundary value problems for some class of ordinary differential equations, Rocky mountain J. math., 10, 35-58, (1980) · Zbl 0476.34017
[6] Gregus, M.; Neumann, F.; Arscott, F.M., Three-point boundary value problems for differential equations, J. London math. soc., 3, 429-436, (1971) · Zbl 0226.34010
[7] Gupta, C.P., Solvability of a three-point boundary value problem for a second order ordinary differential equation, J. math. anal. appl., 168, 540-551, (1992) · Zbl 0763.34009
[8] Kelevdjiev, P., Existence of solutions for two-point boundary value problems, Nonlinear anal., 22, 217-224, (1994)
[9] Kiguradze, I.T.; Lomtatidze, A.G., In certain boundary valve problems for second-order linear ordinary differential equations with singularities, J. math. anal. appl., 101, 325-347, (1984) · Zbl 0559.34012
[10] Marano, S.A., A. remark on a second-order three-point blundary value problem, J. math. anal. appl., 183, 518-522, (1994) · Zbl 0801.34025
[11] Moshinsky, M., Sobre los problemas de condiciones a la frontiera en una dimension de caracteristicas discontinuas, Bol. soc. mat. mexicana, 7, 1-25, (1950)
[12] O’Regan, D., Boundary value problems for second and higher order differential equations, Proc. amer. math. soc., 113, 761-775, (1991) · Zbl 0742.34023
[13] Rodriguez, A.; Tineo, A., Existence theorems for the Dirichlet problem without growth restrictions, J. math. anal. appl., 135, 1-7, (1988) · Zbl 0674.34016
[14] Thomas, J.W.; Zachmann, D.W., A nonlinear three-point boundary value problem, J. math. anal. appl., 58, 647-652, (1977) · Zbl 0357.34012
[15] Timoshenko, S., Theory of elastic stability, (1961), McGraw-Hill New York
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.