Periodic solutions for indefinite singular equations with singularities in the spatial variable and non-monotone nonlinearity

P. AMSTER; M. ZAMORA

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

AMER INST MATHEMATICAL SCIENCES

Lugar: springfield; Año: 2018 vol. 38 p. 4819 - 4835

1078-0947

We prove the existence of $T-$periodic solutions for the second order non-linear equationegin{equation*}left(rac{u´}{sqrt{1-u´^2}} ight)´=h(t)g(u),end{equation*}where the non-linear term $g$ has two singularities and the weight function $h$ changes sign. We find a relation between the degeneracy of the zeroes of the weight function and the order of one of the singularities of the non-linear term. The proof is based on the classical Leray-Schauder continuation theorem. Some applications to important mathematical models are presented.