【摘要】 本文研究Banach空间Lp(Ω)中一类半线性椭圆型方程的不适定边值问题.运用度量广义逆 与Schauder不动点定理证得该问题的最小极值解的存在性,应用Banach空间几何与Sobolev空问的 方法,给出最小极值解的等价条件.本文结果,可应用于奇异最优控制问题.更多还原

【Abstract】 This paper studies the least extremal solutions of ill-posed Neumann boundary value problems for a class of semilinear elliptic equations in Lp(?), The existence of the least extremal solution is proved by the metric generalizea inverse and Schauder fixed point theorem. By means of the mathod of Geometry of Banach space, the equivalent condition of the least extremal solution is given in this paper,which can be applied to the singular control theory.更多还原