Erbe, L. H.; Knobloch, H. W. Boundary value problems for systems of second order differential equations. (English) Zbl 0582.34024 Proc. R. Soc. Edinb., Sect. A 101, 61-76 (1985). We consider boundary value problems for second order differential systems of the form (1) \(x''=A(t)x'+f(t,x)\) and (2) \(x''=A(t)x'+f(t,x)+q(t,x).\) By assuming the existence of a solution \(\hat x=\hat x(t)\) to (1) with \((t,\hat x(t))\in \Omega\), a given region in (t,x) space, we derive conditions under which there exists a solution to (2) which stays in a certain neighbourhood of \(\hat x(\)t) and satisfies given boundary conditions. Cited in 4 Documents MSC: 34B15 Nonlinear boundary value problems for ordinary differential equations Keywords:second order differential systems PDFBibTeX XMLCite \textit{L. H. Erbe} and \textit{H. W. Knobloch}, Proc. R. Soc. Edinb., Sect. A, Math. 101, 61--76 (1985; Zbl 0582.34024) Full Text: DOI