\`x^2+y_1+z_12^34\`
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Existence and multiplicity of periodic solutions to an indefinite singular equation with two singularities. The degenerate case

This research was partially supported by FONDECYT

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  • 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.

    Mathematics Subject Classification: Primary: 34C25, 34B16, 47H11, 70F05.

    Citation:

    \begin{equation} \\ \end{equation}
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  • Figure 1.  Open balls ${\frak{B}}_i$ and connected sets ${\frak{C}}_i$ for i = 1, 2

    Figure 2.  A numerical approximation to a closed orbit of the equation (3) for β = 0.01, with h(t) = sin99 t

    Figure 3.  A numerical approximation to a closed orbit of the equation (3) for β = 0.01, with h(t) = sin99 t

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