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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (11): 1461-1468.doi: https://doi.org/10.1007/s10483-009-1112-z

• Articles • 上一篇    下一篇

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

刘冠琦1 王玉文1 史峻平1,2   

  1. 1. Y. Y. Tseng Functional Analysis Research Center and Department of Mathematics, Harbin Normal University, Harbin 150025, P. R. China;
    2. Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
  • 收稿日期:2009-02-18 修回日期:2009-09-28 出版日期:2009-12-02 发布日期:2009-11-01

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

LIU Guan-Qi1, WANG Yu-Wen1, SHI Jun-Ping1,2   

  1. 1. Y. Y. Tseng Functional Analysis Research Center and Department of Mathematics, Harbin Normal University, Harbin 150025, P. R. China;
    2. Department of Mathematics, College of William and Mary, Williamsburg, VA 23187-8795, USA
  • Received:2009-02-18 Revised:2009-09-28 Online:2009-12-02 Published:2009-11-01

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摘要： 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.

关键词: semilinear equation, Allee effect, positive solutions, existence

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.

Key words: semilinear equation, Allee effect, positive solutions, existence

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