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.

本文涉及对以下一类Choquard型方程的一些分支性质的研究： （P） $$ \ left \ {{\ begin {array} {* {20} {l}} {-\ Delta u = \ lambda f（x）\ left [{u + \ left（{{I_ \ alpha} * f（\ cdot）H（u）} \ right）h（u）} \ right]，{\ rm {in}} \ {{\ mathbb {R}} ^ 3}，} \\ {{{\ lim} _ {| x | \ to \ infty}} u（x）= 0，\ quad u（x）> 0，\ quad x \ in {{\ mathbb {R}} ^ 3}，\ quad u \ in {D ^ {1， 2}}（{{\ mathbb {R}} ^ 3}），} \ end {array}} \ right。$$ 其中 $ {I_ \ alpha}（x）= 1 / | x {| ^ \ alpha} ，\，\ alpha \ in（0,3），\，\ lambda> 0，\，f：{{\ mathbb {R}} ^ 3} \ to {\ mathbb {R}} $ 是一个正连续函数和h： $ {\ mathbb {R}} \ to {\ mathbb {R}} $ 是有界的Hölder连续函数。使用的主要工具是Leray–Schauder学位理论和Rabinowitz导致的全局分歧结果。