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

PABLO AMSTER; MARIEL PAULA KUNA

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS

JULIUSZ SCHAUDER CTR NONLINEAR STUDIES

Año: 2018

1230-3429

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 Painlev´e II equation are extended. It is proved that the uniqueness or multiplicity of solutions depend on the interaction between the mapping$rac {partial g}{partial u}(cdot,0)$  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.