Shekhter, B. L. On a boundary value problem of periodic type for a linear second order ordinary differential equation. (Russian) Zbl 0607.34016 Differ. Uravn. 22, No. 9, 1551-1556 (1986). The boundary value problem (1) \(u''=f(t,u,u'),\) (2) \(u(a)=c_{11}u(b)+c_{12}u'(b)\), \(u'(a)=c_{21}u(b)+c_{22}u'(b),\) is considered; the main result is the following: Suppose that all solutions of (1) are prolongable on [a,b], that \(f(t,x,y)\quad sgn x=- p(t)h(| x|,| y|)+q(t)(| x| +| y|),\) for \(a\leq t\leq b\), \(x^ 2+y^ 2\geq 1\), with suitable p and q and for \(\epsilon\in]0,\pi /2[\), \(\lim \quad (1/\rho)h(\rho \quad \cos \phi,\quad \rho \quad \sin \phi)]=\infty\) uniformly with respect to \(\phi\in [0,\pi /2-\epsilon]\). Then the problem (1),(2) has at least one solution. Reviewer: A.Haimovici MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations 34A30 Linear ordinary differential equations and systems Keywords:second order differential equation; periodic boundary value problem PDFBibTeX XMLCite \textit{B. L. Shekhter}, Differ. Uravn. 22, No. 9, 1551--1556 (1986; Zbl 0607.34016)