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 [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.
Citation
Pablo Amster. Mariel P. Kuna. "On exact multiplicity for a second order equation with radiation boundary conditions." Topol. Methods Nonlinear Anal. 54 (1) 233 - 246, 2019. https://doi.org/10.12775/TMNA.2019.039