Some eigenvalue problems with non-local boundary conditions and applications

Rafael Abreu; Cristian Morales-Rodrigo; Antonio Suárez

doi:10.3934/cpaa.2014.13.2465

Article Contents

2014, Volume 13, Issue 6: 2465-2474. Doi: 10.3934/cpaa.2014.13.2465

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Some eigenvalue problems with non-local boundary conditions and applications

1.
Faculdade de Matemática, Universidade Federal do Pará, Belém
2.
Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Calle Tara s/n, 41012-Seville
3.
Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Univ. de Sevilla, C/. Tarfia s/n, 41012 - Sevilla

Received: November 30, 2013

Revised: March 31, 2014

Published: October 2014

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Abstract

In this paper we study an elliptic eigenvalue problem with non-local boundary condition. We prove the existence of the principal eigenvalue and its main properties. As consequence, we show the existence and uniqueness of positive solution of a nonlinear problem arising from population dynamics.

Keywords:

Non-local boundary condition,
eigenvalue problem.

Mathematics Subject Classification: Primary: 35J60; Secondary: 45K05.

Citation:

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References

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