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- W1585870819 abstract "In this paper, we consider the existence of positive solutions of the degenerate logistic type elliptic equation −Δu=a(x)u−b(x)f(u),x∈RN∖Du|∂D=∞, where N≥2, D⊂RN is a bounded smooth domain and a(x), b(x) are continuous functions on RN with b(x)≥0, b(x)≢0, especially b(x)=0 on ∂D and f(u)∈C(0,∞). We show that under rather general conditions on a(x) and b(x) for large |x| and f(u) behaves like uq where q>1. Without the behavior of b(x) near the boundary ∂D, it will be shown that there exists a unique positive solution. Our results improve the corresponding ones in [W. Dong, Pang, Uniqueness of boundary blow-up solutions on exterior domain of RN, J. Math. Anal. Appl. 330 (2007), 654–664] and [Y. Du, L. Ma, Logistic type equations on RN by a squeezing method involving boundary blow-up solutions, J. London Math. Soc., (2) 64 (2001), 107–124]." @default.
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- W1585870819 date "2009-12-01" @default.
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- W1585870819 title "Uniqueness of boundary blow-up solutions on unbounded domain of" @default.
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- W1585870819 doi "https://doi.org/10.1016/j.na.2009.03.084" @default.
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