某些非线性边值问题的分支性态

ON THE BIFURCATION PROPERTIES OF SOME NONLINEAR BVPS

用奇点理论的方法研究了一类带分支参数λ的非线性边值问题。这类方程形如（ｕ，λ）＝ｕ＂十Ｆ（ｕ，λ）＝０，边值条件形如ａｕ（０）十ｂｕ＇（０）＝０，ｃｕ（１）十ｄｕ＇（１）＝０而其中的非线性项Ｆ（ｕ，λ）是具有分支的余维有限的奇点．得到了这类问题的分支解的存在性及分支解的个数等结果。

One classes of nonlinear boundary value problems with bifurcation parmeter λ arestudied by using singularity theoty. We study the darirentinl equation (u, λ)=u'+F(u, λ)= 0, with the condition of boundary value au (0) + bu' (0)=0 and cu(1) + du'(1) =0, where thenonlinear term F(u,λ ) is a singularity of finite codimension. When the singularity F (u, λ ) satisfies some conditions, the information of the existence and the numbers of the bifurcation solutionsof the nonlinear BVP follows from our results.