The solvability of two linear matrix equations

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The maximal and minimal ranks of A − BXC with applications (2003, result): “The following result was shown in [17]; see also [ 19 ]:”
On solutions to the quaternion matrix equation AXB+CYD=E (2008, unknown): “has been well-studied in matrix theory (see, e.g., [2], [9], [10], [12], [ 14 ], [18]-[21], [35]).”
The general solutions to some systems of matrix equations (2015, background): “In 2000, Tian [18] gave a solvable condition to the system (1.1) in terms of ranks.”
Two special kinds of least squares solutions for the quaternion matrix equation AXB+CXD=E (2012, background): “For example, Mitra [14] and Tian [16] considered the solvability condition for the complex and real matrix equation (1.1), respectively.”
Some matrix equations with applications† (2012, background): “1 Tian in [30] derived the solvability condition of Equation (1.”