Translator Disclaimer
2019 On exact multiplicity for a second order equation with radiation boundary conditions
Pablo Amster, Mariel P. Kuna
Topol. Methods Nonlinear Anal. 54(1): 233-246 (2019). DOI: 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 [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

Download 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

Information

Published: 2019
First available in Project Euclid: 16 July 2019

zbMATH: 07131282
MathSciNet: MR4018278
Digital Object Identifier: 10.12775/TMNA.2019.039

Rights: Copyright © 2019 Juliusz P. Schauder Centre for Nonlinear Studies

JOURNAL ARTICLE
14 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.54 • No. 1 • 2019
Back to Top