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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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