Periodic solutions to second-order indefinite singular equations.

The efficient conditions guaranteeing the existence of a T -periodic solution to the second order differential equation u ″ = h ( t ) g ( u ) are established in the paper. Here, g is a positive and decreasing function which has a strong singularity at the origin, and the weight h ∈ L ( R / T Z ) is a sign-changing function. The obtained results have the form of relation between the multiplicities of the zeroes of the weight function h and the order of the singularity of the nonlinear term. The approach is based on Leray–Schauder degree theory, proving that no T -periodic solution of a certain homotopy appears on the boundary of an unbounded open set during the deformation to an autonomous problem. [ABSTRACT FROM AUTHOR]