一类非线性算子方程解的存在性

EXISTENCE OF SOLUTIONSFOR A CLASS OF NON-LINEAR OPERATOR EQUATIONS

本文建立了非线性算子方程ｘ＝ｘ＿０＋（Ｌｘ）（Ａｘ）解的存在定理，其中Ｌ和Ａ是从Ｂａｎａｃｈ代数Ｅ到Ｅ的非线性算子。然后，运用这些结果研究了非线性ＣｈａｎｄｒａｓｅｋｈａｒＨ－方程连续正解（或负解）的存在性，所得结果改进或推广了ＲｉｃｈａｒｄＷＬｅｇｇｅｔｔ，Ｓｔｕ－ａｒｔＣＡ和本文作者的一些已知结果。

In this paper, we establish some existence theorems for a class of non- linear operator equation x =x0+(Lx)(Ax)Where L;E→E and A:E→E are both non- linear operators and E is a Banach algebra. As well,we use the results to study the existence of poitive(ot negative)solutions in C(G)’for the non-linear Chandrasekhar H-equationOur results improve and generalize some known results of Richard W,Leggett,C. A. Stuart and the authors.