Moore-Penrose Inverse and Semilinear Equations

• 作者: Hugo Leiva Raúl Manzanilla
• 来源期刊: 线性代数与矩阵理论研究进展(英文)
• 学科: 数学
• 关键词: SEMILINEAR EQUATIONS Moore-Penrose INVERSE Rothe’s Fixed POINT THEOREM
• 年，卷（期）: 2018,（1）
• 页码范围: 11-17
• 页数: 7页
• 分类号: O1

摘要

In this paper, we study the existence of solutions for the semilinear equation , where A is a , , and is a nonlinear continuous function. Assuming that the Moore-Penrose inverse AT(AAT)-1?exists (A denotes the transposed matrix of A) which is true whenever the determinant of the matrix AAT is different than zero, and the following condition on the nonlinear term satisfied . We prove that the semilinear equation has solutions for all. Moreover, these solutions can be found from the following fixed point relation .