Periodic solutions of systems with singularities of repulsive type

PABLO AMSTER; MANUEL MAURETTE

ADVANCED NONLINEAR STUDIES

ADVANCED NONLINEAR STUDIES, INC

Lugar: San Antonio, Texas, Estados Unidos; Año: 2011 vol. 11 p. 201 - 220

1536-1365

Motivated by the classical Coulomb central motion model, we study the existence of $T$-periodic solutions for the nonlinear second order system of singular ordinary differential equations $u´´+g(u)=p(t)$. Using topological degree methods, we prove that when the nonlinearity g defined on R^N-{0} is continuous, repulsive at the origin and bounded at infinity, if an appropriate Nirenberg type condition holds then either the problem has a classical solution, or else there exists a family of solutions of perturbed problems that converges uniformly and weakly in $H^1$ to some limit function $u$. Furthermore, under appropriate conditions we prove that $u$ is a classical solution.