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.


34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
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[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
[2] Mawhin, J., Topological Degree Methods in Nonlinear Boundary Value Problems (1979), CBMS 40: CBMS 40 Providence, RI · Zbl 0414.34025
[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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