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Multiplicity results for four-point boundary value problems. (English) Zbl 0756.34026

Let \(I:=[a,b]\) and \(f: I\times\mathbb R^ 2\to\mathbb R\). The equation (1) \(u''(t)+f(t,u,u')=s\), \(t\in I\), where \(s\in\mathbb R\) is a parameter, with conditions (2) \(u(a)=u(c)\), \(u(d)=u(b)\), where \(c\leq d\) and \(c\), \(d\in I\), is considered. Under Bernstein-Nagumo conditions existence and number of solutions with respect to the parameter \(s\) of the problem (1), (2) is studied.

MSC:

34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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References:

[1] Fabry, C.; Mawhin, J.; Nkashama, M. N., A multiplicity result for periodic solutions of forced nonlinear second order ordinary differential equations, Bull. London Math. Soc., 18, 173-180 (1986) · Zbl 0586.34038
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[3] Nkashama, M. N., A generalized upper and lower solutions method and multiplicity results for periodic solutions of nonlinear first order ordinary differential equations, J. math. Analysis Applic., 140, 381-395 (1989) · Zbl 0674.34009
[4] Nkashama, M. N.; Santanilla, J., Existence of multiple solutions for some nonlinear boundary value problems, J. diff. Eqns, 84, 148-164 (1990) · Zbl 0693.34011
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