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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
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##### 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
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