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Advanced Nonlinear Studies

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Non-local Degenerate Diffusion Coefficients Break Down the Components of Positive Solutions

M. Delgado
  • Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain
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/ C. Morales-Rodrigo
  • Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain
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/ J. R. Santos Júnior / A. Suárez
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  • Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Universidad de Sevilla, Sevilla, Spain
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Published Online: 2019-05-08 | DOI: https://doi.org/10.1515/ans-2019-2046

Abstract

This paper deals with nonlinear elliptic problems where the diffusion coefficient is a degenerate non-local term. We show that this degeneration implies the growth of the complexity of the structure of the set of positive solutions of the equation. Specifically, when the reaction term is of logistic type, the continuum of positive solutions breaks into two disjoint pieces. Our approach uses mainly fixed point arguments.

Keywords: Non-local Diffusion; Degenerate Coefficient; Continuum of Positive Solutions

MSC 2010: 35J60; 35J70; 35J15

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About the article


Received: 2019-03-28

Accepted: 2019-04-04

Published Online: 2019-05-08


Funding Source: MINECO/FEDER/UE

Award identifier / Grant number: MTM2015-69875-P

Funding Source: CNPq

Award identifier / Grant number: 302698/2015-9

Funding Source: CAPES

Award identifier / Grant number: 88881.120045/2016-01

M. Delgado, C. Morales-Rodrigo and A. Suárez were partially supported by MTM2015-69875-P (MINECO/ FEDER, UE). J. R. Santos Júnior was partially supported by CNPq-Proc. 302698/2015-9 and CAPES-Proc. 88881.120045/2016-01, Brazil.


Citation Information: Advanced Nonlinear Studies, ISSN (Online) 2169-0375, ISSN (Print) 1536-1365, DOI: https://doi.org/10.1515/ans-2019-2046.

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