On four-point regular BVPs for second-order quasi-linear ODEs. (English) Zbl 0769.34019

The authors consider the scalar four-point boundary value problem of the form \(x''=f(t,x,x')\), \(x(a)+px(b)=A\), \(x(c)+qx(d)=B\), where \(A,B,a,b,c\in\mathbb{R}\), \(p,q\in\{-1,0,1\}\) and \(f\) is supposed to be continuous. They prove the existence of solutions using Green’s functions and the Schauder fixed point theorem.


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