Abstract

In this paper, we are concerned with quasilinear elliptic equations with a Dirichlet boundary condition and two parameters. Using the truncation techniques and variational methods, the existence and/or multiplicity of positive solutions to the problems with a nonlinearity which satisfies either logistic growth rate or strong Allee effect growth rate are investigated. Also, a nonexistence result for nonnegative and nontrivial solutions is given.

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