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Multiplicity results for second order nonlinear problems with maximum and minimum. (English) Zbl 0920.34058
Consider the functional boundary value problem \[ x''(t)= [Fx](t),\;t\in J= [a,b],\;\min\{x(t): t\in J\}= \alpha,\;\max\{x(t): t\in J\}= \beta, \] where \(F: C^1(I)\to L^1(I)\) is an operator, and \(\alpha\), \(\beta\) are given real numbers.
A solution is a function \(x\in AC^1(I)\) satisfying the equation for a.e. \(t\in J\) and the boundary conditions. Sufficient conditions for the existence of at least two solutions are presented by using a lemma of Bihari and a Bernstein-Nagumo growth condition.

MSC:
34K10 Boundary value problems for functional-differential equations
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