椭圆型方程组边值问题解的存在性与多解性

讨论了生化系统中的Ｂｒａｓｓｌａｔｏｒ方程与Ｎｏｙｅｓ－Ｆｉｅｌｄ方程所对应的平衡态方程解的存在性及多解问题．利用椭圆型方程的先验估计及经过一些技巧处理，给出了Ｂｒａｓｓｌａｔｏｒ方程组平衡解的一个先验估计，从而利用拓扑度理论证明了其平衡解的存在性．并由上下解方法结合度的计算证明了Ｎｏｙｅｓ－Ｆｉｅｌｄ方程的平衡解的多解性

Existence of solutions for some type of elliptic equations

The paper disusses the existence of steady state solutions of the Brasslator model and the Noyes Field model arising in biochemical systems. An existence theorem is presented for the steady state problem of the Brasslator equations, in term of degree theory and by using some technique in the priori estimate. Furthermore, through suitable construction of upper and lower solutions and the theory of Topology degree, it is shown that there exist two positive steady state solutions for Noyes Field equations.