Topological Methods in Nonlinear Analysis

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

Pablo Amster and Mariel P. Kuna

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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 [2] 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 [2] regarding, on the one hand, the existence of sign-changing solutions and, on the other hand, exact multiplicity are solved.

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Topol. Methods Nonlinear Anal., Volume 54, Number 1 (2019), 233-246.

First available in Project Euclid: 16 July 2019

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Amster, Pablo; Kuna, Mariel P. On exact multiplicity for a second order equation with radiation boundary conditions. Topol. Methods Nonlinear Anal. 54 (2019), no. 1, 233--246. doi:10.12775/TMNA.2019.039.

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