Moore-Penrose Inverse and Semilinear Equations

¹ Yachay Tech, School of Mathematical Sciences and Information Technology, Imbabura, Ecuador

² Yachay Tech, School of Mathematical Sciences and Information Technology, Imbabura, Ecuador

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 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 .

KeywordsSemilinear EquationsMoore-Penrose InverseRothe’s Fixed Point Theorem

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Moore-Penrose Inverse and Semilinear Equations

Abstract

References (7)