Skip to main content
SpringerLink
Log in

Existence of positive solution of a nonlocal logistic population model

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

In this paper, we study the existence of positive solutions for a class of nonlocal problem arising in population dynamic. Basically, we prove our results via bifurcation theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Allegretto W., Nistri P.: On a class of nonlocal problems with applications to mathematical biology. Differential equations with applications to biology (Halifax, NS, 1997), 1–14, Fields Inst. Commun., 21, Am. Math. Soc., Providence, RI (1999)

  2. Chen S., Shi J.: Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect. J. Differential Equations 253, 3440–3470 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  3. Chipot,M.: Remarks on Some Class of Nonlocal Elliptic Problems, Recent Advances on Elliptic and Parabolic Issues, World Scientific, pp. 79–102 (2006)

  4. Corrêa F.J.S.A., Delgado M., Suárez A.: Some nonlinear heterogeneous problems with nonlocal reaction term. Advances in Differential Equations 16, 623–641 (2011)

    MATH  MathSciNet  Google Scholar 

  5. Coville, J.: Convergence to equilibrium for positive solutions of some mutation-selection model. arXiv:1308.647 (2013)

  6. Leman, H., Méléard, S., Mirrahimi, S.: Influence of a spatial structure on the long time behavior of a competitive Lotka-Volterra type system. arXiv:1401.1182 (2014)

  7. Ouyang T.: On the positive solutions of semilinear equations \({\Delta u+\lambda u-hu^{p}=0}\) on the compact manifolds. Trans. Am. Math. Soc. 331, 503–527 (1992)

    MATH  Google Scholar 

  8. Perthame, B.: Transport equations in biology, Transport Equations in Biology, Frontiers in Mathematics, vol. 12, Birkhauser Basel, pp. 1–26 (2007)

  9. Rabinowitz P.: Some global results for nonlinear eigenvalue problems. J. Funct. Anal. 7, 487–513 (1971)

    Article  MATH  MathSciNet  Google Scholar 

  10. Sun L., Shi J., Wang Y.: Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation. Z. Angew. Math. Phys. 64, 1267–1278 (2013)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Unidade Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-900, Campina Grande-PB, Brazil

    Claudianor O. Alves

  2. Departamento de Ecuaciones Diferenciales y Análisis Numérico, Facultad de Matemáticas, Calle Tarfia s/n, 41012, Sevilla, Spain

    Manuel Delgado & Antonio Suárez

  3. Acadêmica de Matemática, Universidade Federal de Campina Grande, 58429-900, Campina Grande-PB, Brazil

    Marco A. S. Souto

Authors
  1. Claudianor O. Alves
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manuel Delgado
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marco A. S. Souto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Antonio Suárez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Antonio Suárez.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Alves, C.O., Delgado, M., Souto, M.A.S. et al. Existence of positive solution of a nonlocal logistic population model. Z. Angew. Math. Phys. 66, 943–953 (2015). https://doi.org/10.1007/s00033-014-0458-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00033-014-0458-x

Mathematics Subject Classification

Keywords

Search

Navigation