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Displaying similar documents to “A New Proof Of Belousov's Theorem For A Special Law Of Quasigroup Operations”

Asymptotic behavior of solutions of nonlinear difference equations

Janusz Migda (2004)

Mathematica Bohemica

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The nonlinear difference equation x n + 1 - x n = a n ϕ n ( x σ ( n ) ) + b n , ( E ) where ( a n ) , ( b n ) are real sequences, ϕ n , ( σ ( n ) ) is a sequence of integers and lim n σ ( n ) = , is investigated. Sufficient conditions for the existence of solutions of this equation asymptotically equivalent to the solutions of the equation y n + 1 - y n = b n are given. Sufficient conditions under which for every real constant there exists a solution of equation () convergent to this constant are also obtained.