半线性椭圆型方程的狄氏问题的正解的最大歧点和最大渐近歧点

Greadest Bifurcation and Asymptotic Bifurcation Point of Positive Solutions for semilinear Elliptic partial Differential Equation

本文利用作者在[1]中提供的一个不动点指数计算公式,导出全连续锥算子最大歧点定理和最大渐近歧点定理。然后将这个抽象结果应用于二阶半线性椭圆型方程的狄氏问题,找出其正解的最大歧点和最大渐近歧点。

In the present paper we deduce the Greadest Bifurcation and Asymptotic Bifurcation Point Theorem of a complete continuous cone operation using the computational formala of fixed point index in the referencei [1], and then we use those re- sults to the Dirichlet Problem of a second order semilinear elliptic partial differential equation and obtain greadest bifurcation and asymptotic bifurcation point of positive so- lutions for this problem.