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Boundary value problems for second-order differential equations on unbounded domains in a Banach space. (English) Zbl 1035.34015

The author studies the following two-point boundary value problem for a second-order nonlinear differential equation in a Banach space X

d 2 x dt 2 =ft , x (t) , dx(t) dt,t0,x(t)=x 0 ,dx() dt=y ,

where x 0 ,y X are given vectors, and f:[0,)×X×XX 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.

MSC:
34B40Boundary value problems for ODE on infinite intervals
34B20Weyl theory and its generalizations