Subharmonic bouncing solutions of generalized Lazer-Solimini equation

The paper deals with the singular differential equation x 00 + g(x) = p(t), with g having a weak singularity at x = 0 and 2π-periodic function p. For any positive integers m and n, the coexistence of 2mπ-periodic bouncing solutions having n impacts with the singularity and a classical positive periodic solution is proven