On bounded solutions of some classes of two-parameter difference equations in a Banach space
The authors study some classes of difference equations for vector-valued functions, for example, the equation NEWLINE\[NEWLINE u(m,n)=Au(m,n-1)+Bu(m-1,n)+Cu(m-1,n-1)+v(m,n),\;\;m\geq 1,\;n\geq 1, NEWLINE\]NEWLINE where \(A,B,C\) are bounded operators and the vector-functions \(v(m,n)\), \(u(m,0)\), \(u(0,n)\) are given. Necessary and sufficient conditions for the existence and uniqueness of a bounded solution are proposed.
scientific article; zbMATH DE number 1631381