Spiraling bifurcation diagrams in superlinear indefinite problems

Julián López-Gómez; Marcela Molina-Meyer; Andrea Tellini

doi:10.3934/dcds.2015.35.1561

Article Contents

2015, Volume 35, Issue 4: 1561-1588. Doi: 10.3934/dcds.2015.35.1561

This issue Previous Article Invasion entire solutions in a competition system with nonlocal dispersal Next Article Pattern formation in a cross-diffusion system

Spiraling bifurcation diagrams in superlinear indefinite problems

1.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040-Madrid
2.
Departamento de Matemáticas, Universidad Carlos III de Madrid Campus de Leganés, Avda. Universidad 30, 28911 Leganés, Madrid
3.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, Plaza de Ciencias 3, 28040 Madrid

Received: July 31, 2013

Revised: March 31, 2014

Published: May 2017

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Abstract

This paper computes and discusses a series of intricate global bifurcation diagrams for a class of one-dimensional superlinear indefinite boundary value problems arising in population dynamics, under non-homogeneous boundary conditions, measured by $M>0$; the main bifurcation parameter being the amplitude $b$ of the superlinear terms.

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Mathematics Subject Classification: 65N35, 65P30, 65N22.

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