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On some modification of the Levinson operator and its application to a three-point boundary value problem. (English) Zbl 0756.34024

The author considers the three-point boundary value problem \(x''=f(t,x)\), \(x(0)=x(a)=x(2a)\), \(a\in\mathbb{R}\), \(a\neq 0\), where \(f\) is a continuous function. Under the assumption \(\liminf_{| x|\to\infty}f(t,x)\cdot\text{sgn} x>0\) he proves the existence of a solution. The method of proofs is based on the Borsuk antipodal theorem for some modified Levinson operator.

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:

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