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.


34B10 Nonlocal and multipoint boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
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