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- W2156347921 abstract "In this paper, we consider the nonhomogeneous semilinear elliptic equation , where λ ≥ 0, 1 < p < ( N + 2)/( N − 2), if N ≥ 3, 1 < p < ∞, if N = 2, h(x) ∈ H −l (ℝ N ), 0 ≢ h(x) ≥ 0 in ℝ N , K(x) is a positive, bounded and continuous function on ℝ N . We prove that if K(x) ≥ K ∞ > 0 in ℝ N , and lim ∣x∣⃗∞ K(x) = K ∞ , then there exists a positive constant λ ✶ such that (✶) λ has at least two solutions if λ ∈ (0, λ ✶ ) and no solution if λ > λ ✶ . Furthermore, (✶) λ has a unique solution for λ = λ ✶ provided that h(x) satisfies some suitable conditions. We also obtain some further properties and bifurcation results of the solutions of (1.1) λ at λ = λ ✶ ." @default.
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- W2156347921 date "2005-12-01" @default.
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- W2156347921 title "Bifurcation of positive entire solutions for a semilinear elliptic equation" @default.
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- W2156347921 doi "https://doi.org/10.1017/s0004972700035188" @default.
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