This paper concerns the study of some bifurcation properties for the following class of Choquard-type equations: (P) $$\left\{ {\begin{array}{*{20}{l}} { - \Delta u = \lambda f(x)\left[ {u + \left( {{I_\alpha }*f( \cdot )H(u)} \right)h(u)} \right],{\rm{ in }} \ {{\mathbb{R}}^3},}\\ {{{\lim }_{|x| \to \infty }}u(x) = 0,\quad u(x) > 0,\quad x \in {{\mathbb{R}}^3},\quad u \in {D^{1,2}}({{\mathbb{R}}^3}),} \end{array}} \right.$$ where ${I_\alpha }(x) = 1/|x{|^\alpha },\,\alpha \in (0,3),\,\lambda > 0,\,f:{{\mathbb{R}}^3} \to {\mathbb{R}}$ is a positive continuous function and h : ${\mathbb{R}} \to {\mathbb{R}}$ is a bounded Hölder continuous function. The main tools used are Leray–Schauder degree theory and a global bifurcation result due to Rabinowitz.

中文翻译：

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整个 ℝ3 一类 CHOQUARD 方程的分岔性质

本文涉及对以下类别的 Choquard 型方程的一些分岔性质的研究：(磷)$$\left\{ {\begin{array}{*{20}{l}} { - \Delta u = \lambda f(x)\left[ {u + \left( {{I_\alpha }*f ( \cdot )H(u)} \right)h(u)} \right],{\rm{ in }} \ {{\mathbb{R}}^3},}\\ {{{\lim } _{|x| \to \infty }}u(x) = 0,\quad u(x) > 0,\quad x \in {{\mathbb{R}}^3},\quad u \in {D^{1, 2}}({{\mathbb{R}}^3}),} \end{array}} \right.$$在哪里${I_\alpha }(x) = 1/|x{|^\alpha },\,\alpha \in (0,3),\,\lambda > 0,\,f:{{\mathbb{R }}^3} \to {\mathbb{R}}$是一个正连续函数并且H：${\mathbb{R}} \to {\mathbb{R}}$是有界 Hölder 连续函数。使用的主要工具是 Leray-Schauder 度数理论和 Rabinowitz 的全局分岔结果。