On exact multiplicity for a second order equation with radiation boundary conditions

Pablo Amster, Mariel P. Kuna

DOI: http://dx.doi.org/10.12775/TMNA.2019.039

Abstract


A second order ordinary differential equation with a superlinear term $g(x,u)$ under radiation boundary conditions is studied. Using a shooting argument, all the results obtained in the previous work \cite{AKR3} for a Painlevé II equation are extended. It is proved that the uniqueness or multiplicity of solutions depend on the interaction between the mapping $\frac {\partial g}{\partial u}(\cdot,0)$ and the first eigenvalue of the associated linear operator. Furthermore, two open problems posed in \cite{AKR3} regarding, on the one hand, the existence of sign-changing solutions and, on the other hand, exact multiplicity are solved.

Keywords


Second order ODEs; radiation boundary conditions; multiple solutions; electro-diffusion models

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References


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