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Moore-Penrose Inverse and Semilinear Equations

DOI: 10.4236/alamt.2018.81002, PP. 11-17

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

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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)-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 \"\".

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