科研之友
微信
新浪微博
Facebook
分享链接
摘要
In this paper, we consider the the second-order ordinary differential equation with periodic boundary problem -(sic)(t) = f (t, x(t)), subject to x(0) - x(2 pi) = (x) over dot(0) - (x) over dot(2 pi) = 0, where f : C([0, 2 pi] x R, R). The operator K = (-d(2)/dt(2) + I)(-1) plays an important role. By using Morse index, Leray-Schauder degree and Morse index theorem of the type Lazer-Solimini, we obtain that the equation has at least two or three nontrivial solutions without assuming nondegeneracy of critical points and has at least four nontrivial solutions assuming nondegeneracy of critical points.
