Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 1, Pages 41-50
doi:10.1155/S1048953300000058
Abstract
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 the
2π-periodic problem for the scalar equation x″+n2x=g(|x|)+f(t,x)+b(t) with bounded g(u) and f(t,x)→0 as |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.