主部单调算子的二择一定理及应用

THE ALTERNATIVE THEOREM OF MONOTONE OPERATOR AND ITS APPLICATIONS

文中证明了当A为单调算子或拟A-proper算子时,有下述二择一结论成立,即或方程Ax-λBx=0有分歧,或当‖f‖足够小时,方程Ax-Bx=f必有解,然后将此结果用于一类二阶拟线性椭园偏微分方程边值问题。

In this paper we proved that, when A is a monotone operator or an A-proper map, either the equation Ax-λBx =0 has a bifurcation or the equation Ax-Bx=f has a solution if ||f|| is small enough. We applied the result to a kind of boundary value pro-blem of quasilinear elliptic partial differential equations of second order.