Existence of a unique bounded solution to a linear second-order difference equation and the linear first-order difference equation
نویسندگان
چکیده
منابع مشابه
General solution to a higher-order linear difference equation and existence of bounded solutions
xn+k – qnxn = fn, n ∈N0, where k ∈N, (qn)n∈N0 , (fn)n∈N0 ⊂C, in the case qn = q, n ∈N0, q ∈C \ {0}. Using the formula, we show the existence of a unique bounded solution to the equation when |q| > 1 and supn∈N0 |fn| <∞ by finding a solution in closed form. By using the formula for the bounded solution we introduce an operator that, together with the contraction mapping principle, helps in showi...
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ژورنال
عنوان ژورنال: Advances in Difference Equations
سال: 2017
ISSN: 1687-1847
DOI: 10.1186/s13662-017-1227-x