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Zbl 1035.34015
Liu, Yansheng
Boundary value problems for second-order differential equations on unbounded domains in a Banach space.
(English)
[J] Appl. Math. Comput. 135, No. 2-3, 569-583 (2003). ISSN 0096-3003

The author studies the following two-point boundary value problem for a second-order nonlinear differential equation in a Banach space $X$ $$\frac{d^2 x}{dt^2}=f \biggl(t, x(t), \frac{d x(t)}{dt}\biggr),\quad t\geq 0, \qquad x(t)=x_0, \quad \frac{d x(\infty)}{dt}=y_\infty,$$ where $x_0, y_\infty\in X$ are given vectors, and $f: [0,\infty)\times X\times X\to X$ is a given continuous function. By virtue of the Sadovskii fixed-point theorem, the existence of solutions is investigated. Besides, the Lipschitz condition for $f$ is not required.
[Michael I. Gil' (Beer-Sheva)]
MSC 2000:
*34B40 Boundary value problems on infinite intervals
34B20 Weyl theory and its generalizations

Keywords: boundary value problem; fixed-point theorem; noncompactness measure

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