On bounded solutions of some classes of two-parameter difference equations in a Banach space (Q2730510)
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scientific article; zbMATH DE number 1631381
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On bounded solutions of some classes of two-parameter difference equations in a Banach space |
scientific article; zbMATH DE number 1631381 |
Statements
8 August 2001
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difference equation
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bounded solution
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On bounded solutions of some classes of two-parameter difference equations in a Banach space (English)
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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.
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