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Boundary and periodic value problems for systems of nonlinear second order differential equations. (English) Zbl 0790.34022
The author considers the boundary and periodic value problem for system of nonlinear second order differential equations \(x''(t)=f(t,x(t),x'(t))\) a.e. \(t \in[0,1]\), \(x \in BC\), where \(f:[0,1] \times \mathbb{R}^{2n} \to \mathbb{R}^ n\) is a Carathéodory function and \(BC\) denotes a boundary condition such as non-homogeneous Dirichlet, Neumann, Sturm-Liouville conditions, or the periodic condition. Existence results are obtained on assumptions which are generalizations of the conventional assumptions for such problems. The proofs rely on the Schauder fixed point theorem.

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34L30 Nonlinear ordinary differential operators
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