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Boundary value problems for doubly perturbed first order ordinary differential systems. (English) Zbl 1118.34011

The paper is devoted to the study of solutions \(x:[0,1]\to \mathbb{R}^n\) of the system \[ x'(t)=A(t)x(t)+F(t,x(t)) + G(t,x(t))\;\; t\in [0,1] \]
satisfying the boundary condition
\[ Mx(0)+Nx(1)=\eta. \]
Existence of solutions is proved under appropriate conditions, using a fixed point theorem for the sum of a contraction and a compact operator.

MSC:

34B15 Nonlinear boundary value problems for ordinary differential equations
34D10 Perturbations of ordinary differential equations
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