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

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


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 

Chinese Library Classification


2000 Mathematics Subject Classification

35B32 35J25 


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Copyright information

© Shanghai University and Springer Berlin Heidelberg 2009

Authors and Affiliations

  • Guan-qi Liu (刘冠琦)
    • 1
  • Yu-wen Wang (王玉文)
    • 1
  • Jun-ping Shi (史峻平)
    • 1
    • 2
  1. 1.Y. Y. Tseng Functional Analysis Research Center and Department of MathematicsHarbin Normal UniversityHarbinP. R. China
  2. 2.Department of MathematicsCollege of William and MaryWilliamsburgUSA

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