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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.

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