TITLE:
Moore-Penrose Inverse and Semilinear Equations
AUTHORS:
Hugo Leiva, Raúl Manzanilla
KEYWORDS:
Semilinear Equations, Moore-Penrose Inverse, Rothe’s Fixed Point Theorem
JOURNAL NAME:
Advances in Linear Algebra & Matrix Theory,
Vol.8 No.1,
January
17,
2018
ABSTRACT: 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)-1exists (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 .