In this paper we study the existence of solution for the following class ofsystem of elliptic equations $$ \left\{ \begin{array}{lcl} -\Delta u=\left(a-\int_{\Omega}K(x,y)f(u,v)dy\right)u+bv,\quad \mbox{in}\quad \Omega -\Delta v=\left(d-\int_{\Omega}\Gamma(x,y)g(u,v)dy\right)v+cu,\quad \mbox{in}\quad \Omega u=v=0,\quad \mbox{on} \quad \partial\Omega \end{array} \right. \eqno{(P)} $$ where $\Omega\subset\R^N$ is a smooth bounded domain, $N\geq1$, and$K,\Gamma:\Omega\times\Omega\rightarrow\R$ is a nonnegative function checkingsome hypotheses and $a,b,c,d\in\R$. The functions $f$ and $g$ satisfy someconditions which permit to use Bifurcation Theory to prove the existence ofsolution for $(P)$.
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机译：在本文中，我们研究以下一类椭圆方程组的解的存在性$$ \ left \ {\ begin {array} {lcl}-\ Delta u = \ left（a- \ int _ {\ Omega} K（x ，y）f（u，v）dy \ right）u + bv，\ quad \ mbox {in} \ quad \ Omega-\ Delta v = \ left（d- \ int _ {\ Omega} \ Gamma（x，y ）g（u，v）dy \ right）v + cu，\ quad \ mbox {in} \ quad \ Omega u = v = 0，\ quad \ mbox {on} \ quad \ partial \ Omega \ end {array} \对。 \ eqno {（P）} $$，其中$ \ Omega \ subset \ R ^ N $是一个光滑有界域，$ N \ geq1 $和$ K，\ Gamma：\ Omega \ times \ Omega \ rightarrow \ R $是检验某些假设和$ a，b，c，d \ in \ R $的非负函数。函数$ f $和$ g $满足一些条件，这些条件允许使用分歧理论证明$（P）$的解的存在。
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