NONCONSTANT PERIODIC SOLUTIONS OF NONLINEAR DIFFERENTIAL EQUATIONS.

摘要

Let g:R('n) (--->) R('n) be of class C' and satisfy g(0) = 0. Assume that g is asymptotically linear at infinity and satisfies a certain weak monotonicity condition. Sufficient conditions for the existence of nonconstant periodic solutions of the second order differential system x''(t) + g(x(t)) = 0 are given. The bulk of our proof consists of establishing spectral properties of certain nonselfadjoint compact linear operators.