Periodic solutions of systems with asymptotically evennonlinearities

[摘要] New conditions of solvability based on a general theorem on the calculation of the index at infinity for vector fields that have degenerate principal linear part as well as degenerate “next order” terms are obtained for the2π-periodic problem for the scalar equationx″+n2x=g(|x|)+f(t,x)+b(t)with boundedg(u)andf(t,x)→0as|x|→0. The result is also applied to the solvability of a two-point boundary value problem and to resonant problems for equations arising in control theory.

[学科分类] 应用数学