Subharmonic bouncing solutions of generalized Lazer–Solimini equation

摘要

The paper deals with the singular differential equation?x′′+g(x)=p(t)x″+g(x)=p(t), with?gg?having a weak singularity at?x=0x=0?and?2π2π-periodic function?pp. For any positive integers?mm?and?nn, the coexistence of?2mπ2mπ-periodic bouncing solutions having?nn?impacts with the singularity and a~classical positive periodic solution is proven.