【摘要】 本文证明了非线性算子方程的某些三解定理和锐角原理,改进和补充了[1]中的结果。更多还原

【Abstract】 Suppose f(x) is a bounded C~1 functional defined on a Hilbert space X, Ax=f′(x).Let In this paper we prove:Theorem 1 Suppose <ⅰ> A satisfies if x_n→x, Ax_n→0,then {x_n} has a convergent subsequenee; <ⅱ> (Ax,x)>0; <ⅲ> (Ax, x )<0.Then Ax=0 has three solutions.Theorem 4 Suppose <ⅰ> A satisfies if Ax_n→0, then ; <ⅱ> (Ax, x )≥0. Then Ax=0 has at least one solution.更多还原