# American Institute of Mathematical Sciences

July  2019, 39(7): 4137-4156. doi: 10.3934/dcds.2019167

## Existence and multiplicity of periodic solutions to an indefinite singular equation with two singularities. The degenerate case

 1 Departamento de Matemática, Grupo de investigación en Sistemas Dinámicos y aplicaciones (GISDA), Universidad del Bo-Bo, Casilla 5-C, Concepción, Chile 2 Departamento de Matemática, Grupo de investigación en Sistemas Dinámicos y aplicaciones (GISDA), C/Federico Garca Lorca, n°18, Oviedo, Spain

Received  October 2018 Published  April 2019

Fund Project: This research was partially supported by FONDECYT.

We analyze the existence of T−periodic solutions to the second-order indefinite singular equation
 $u'' = \beta \frac{{h\left( t \right)}}{{{{\cos }^2}u}}$
which depends on a positive parameter β > 0. Here, h is a sign-changing function with h = 0 and where the nonlinear term of the equation has two singularities. For the first time, the degenerate case is studied, displaying an unexpected feature which contrasts with the results known in the literature for indefinite singular equations.
Citation: José Godoy, Nolbert Morales, Manuel Zamora. Existence and multiplicity of periodic solutions to an indefinite singular equation with two singularities. The degenerate case. Discrete & Continuous Dynamical Systems, 2019, 39 (7) : 4137-4156. doi: 10.3934/dcds.2019167
##### References:

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##### References:
Open balls ${\frak{B}}_i$ and connected sets ${\frak{C}}_i$ for i = 1, 2
A numerical approximation to a closed orbit of the equation (3) for β = 0.01, with h(t) = sin99 t
A numerical approximation to a closed orbit of the equation (3) for β = 0.01, with h(t) = sin99 t
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