×

zbMATH — the first resource for mathematics

On an \(m\)-point boundary value problem. (English) Zbl 0895.34014
An existence theorem for \(m\)-point boundary value problems with a nonlinear growth term is proved: \[ x''(t)=f \bigl(t,x(t),x'(t)\bigr) +y(t), \] \[ x'(0)= 0,\;x(1) =\sum^{m-2}_{i=1} a_ix(\xi_i), \] where \(f:[0,1] \times \mathbb{R}^2 \to\mathbb{R}\) is a continuous function, \(y:[0,1] \to\mathbb{R}\) is bounded, all \(a_i\in \mathbb{R}\) for \(i=1,\dots,m-2\) have the same sign, and \(0<\xi_1 <\xi_2< \cdots< \xi_{m-2} <1\).

MSC:
34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] FENG W. & WEBB J.R.L., Solvability of three-point boundary value problems at resonance, these Proceedings. · Zbl 0891.34019
[2] Gupta, C.P.; Ntouyas, S.K.; Tsamatos, P.C.H., On an m-point boundary-value problem for second-order ordinary differential equations, Nonlinear analysis, TMA, 23, 1427-1436, (1994) · Zbl 0815.34012
[3] Gupta, C.P.; Ntouyas, S.K.; Tsamatos, P.C.H., Solvability of an m-point boundary value problem for second order ordinary differential equations, J. math. anal. appl., 189, 575-584, (1995) · Zbl 0819.34012
[4] Gupta, C.P., Existence theorems for a second order m-point boundary value problem at resonance, Int. J. math. & math sci., 18, 705-710, (1995) · Zbl 0839.34027
[5] Gupta, C.P., A Dirichlet type multi-point boundary value problem for second order ordinary differential equations, Nonlinear analysis, TMA, 26, 925-931, (1996) · Zbl 0847.34018
[6] Il’in, V.; Moiseev, E., Nonlocal boundary value problem of the first kind for a Sturm-Liouville operator in its differential and finite difference aspects, Differential equations, 23, 803-810, (1987) · Zbl 0668.34025
[7] Petryshyn, W.V., Solvability of various boundary value problems for the equation χ″ = f (t,χ,χ′,χ″) − y, Pacific J. math., 122, 169-195, (1986) · Zbl 0585.34020
[8] Mawhin, J., Topological degree and boundary value problems for nonlinear differential equations, (), 74-142 · Zbl 0798.34025
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.