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

@inproceedings{Liu2009ExistenceAN,
  title={Existence and nonexistence of positive solutions of semilinear elliptic equation with inhomogeneous strong Allee effect},
  author={Guan-qi Liu and Yuwen Wang and Junping Shi},
  year={2009}
}
In this paper, we study the equation { ∆u + λf(x, u) = 0 in Ω, u = 0 on ∂Ω, where f(x, u) is sign-changing and inhomogeneous in x. This type of problem arises from the studies of spatial ecology and f(x, u) is a growth pattern called strong Allee effect. We prove that the equation has at least two positive solutions for large λ if ∫ c(x) 0 f(x, s)ds > 0 for x in an open subset of Ω via variational methods. We also prove some nonexistence results. 
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