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Boundary value problems for systems of second order differential equations. (English) Zbl 0582.34024

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.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
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