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Green’s functions for periodic and anti-periodic BVPs to second-order ODEs. (English) Zbl 0795.34013
The paper deals with the second order BVP \(x''+kx= f(t,x,x')\), \(f\in C([0,T] \times\mathbb{R}^ 2)\), \(x(0)+ px(T)=0\), \(x'(0)+ qx'(T)=0\), where \(p,q\in \{-1,1\}\), \(k\in\mathbb{R}\). Using the explicit form of the Green function and the Schauder fixed point theorem, the authors prove the existence of at least one solution of the above BVP.

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