On the range of certain pendulum-type equations

[摘要] Let us consider the BVP mx (t) + g(1)(x'(t)) = f(t), t is an element of [0,T] x(0) = x(T), x'(0) = x'(T), where g(1) is a continuous function. The range R-1 of the operator related to this problem is very well known. In this paper we treat the perturbed problem mx (t) + g(1)(x'(t)) + g(0)(x(t)) = f(t), t is an element of [0, T] x(0)= x(T), x'(0) = x'(T), where go is of pendulum type, showing that, in general, the range of the perturbed operator is not contained in R-1. This points out an important qualitative difference with respect to the case where g(0) is of the Landesmann-Lazer type. On the other hand we prove that if f is small then the mentioned inclusion is true in general. (C) 2000 Academic Press.

[发布日期] 2000-09-15

[关键词] nonlinear boundary value problems;nonlinear damping;bounded nonlinearities;pendulum equation