Author(s)

Hugo Leiva, Raúl Manzanilla

Yachay Tech, School of Mathematical Sciences and Information Technology, Imbabura, Ecuador.

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 A^T(AA^T)^-1 exists (A denotes the transposed matrix of A) which is true whenever the determinant of the matrix AA^T 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 .

Semilinear Equations, Moore-Penrose Inverse, Rothe’s Fixed Point Theorem

Leiva, H. and Manzanilla, R. (2018) Moore-Penrose Inverse and Semilinear Equations. Advances in Linear Algebra & Matrix Theory, 8, 11-17. doi: 10.4236/alamt.2018.81002.