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Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect

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Abstract

In this paper, we study a semilinear elliptic equation defined on a bounded smooth domain. This type of problem arises from the study of spatial ecology model, and the growth function in the equation has a strong Allee effect and is inhomogeneous. We use variational methods to prove that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. We also prove some nonexistence results.

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Authors and Affiliations

  1. Y. Y. Tseng Functional Analysis Research Center and Department of Mathematics, Harbin Normal University, Harbin, 150025, P. R. China

    Guan-qi Liu  (刘冠琦), Yu-wen Wang  (王玉文) & Jun-ping Shi  (史峻平)

  2. Department of Mathematics, College of William and Mary, Williamsburg, VA, 23187-8795, USA

    Jun-ping Shi  (史峻平)

Authors
  1. Guan-qi Liu  (刘冠琦)
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  2. Yu-wen Wang  (王玉文)
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  3. Jun-ping Shi  (史峻平)
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Corresponding author

Correspondence to Jun-ping Shi  (史峻平).

Additional information

Communicated by Ji-bin LI

Project supported by the National Natural Science Foundation of China (No. 10671049) and the USNSF grants (No. DMS-0314736)

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Liu, Gq., Wang, Yw. & Shi, Jp. Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect. Appl. Math. Mech.-Engl. Ed. 30, 1461–1468 (2009). https://doi.org/10.1007/s10483-009-1112-z

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  • DOI: https://doi.org/10.1007/s10483-009-1112-z

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