Abstract Our purpose in this paper is to study positive solutions of the Lane–Emden equation - Δ ⁢ u = V ⁢ u p in ⁢ ℝ N ∖ { 0 } , -\Delta u=Vu^{p}\quad\text{in }\mathbb{R}^{N}\setminus\{0\}, perturbed by a nonhomogeneous potential V, with p ∈ ( N N - 2 , p c ) p\in(\frac{N}{N-2},p_{c}) , where p c {p_{c}} is the Joseph–Ludgren exponent. We construct a sequence of fast and slow decaying solutions with appropriated restrictions for V.

中文翻译：

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包含非齐次势的 Lane-Emden 方程的快慢衰减解

摘要 本文的目的是研究 Lane-Emden 方程的正解 - Δ ⁢ u = V ⁢ up in ⁢ ℝ N ∖ { 0 } , -\Delta u=Vu^{p}\quad\text{in }\mathbb{R}^{N}\setminus\{0\}，被非齐次势 V 扰动，p ∈ ( NN - 2 , pc ) p\in(\frac{N}{N-2}, p_{c}) ，其中 pc {p_{c}} 是 Joseph-Ludgren 指数。我们构造了一系列快速和慢速衰减的解决方案，并对 V 进行适当的限制。