A General Result to the Existence of a Periodic Solution to an Indefinite Equation with a Weak Singularity

摘要

Efficient conditions guaranteeing the existence of a T - periodic solution to the second order differential equation u = h( t) u.,.. ( 0, 1), are established. Here, h. L( R/ TZ) is a rather general sign- changing function with h 0. In contrast with the results in Godoy and Zamora ( Proc R Soc Edinb Sect A Math) and Hakl and Zamora ( J Differ Equ 263: 451- 469, 2017), the key ingredient to solve the aforementioned problem seems to be connected more with the oscillation and the symmetry aspects of the weight function h than with the multiplicity of its zeroes. Roughly speaking, the solvability for the above- mentioned problem can be guaranteed when H+ H- and H+ is large enough.