Classification and existence of positive solutions of fourth-order nonlinear difference equations (Q1041389)
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scientific article; zbMATH DE number 5641523
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Classification and existence of positive solutions of fourth-order nonlinear difference equations |
scientific article; zbMATH DE number 5641523 |
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Classification and existence of positive solutions of fourth-order nonlinear difference equations (English)
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2 December 2009
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The author studies the asymptotic properties of solutions of the fourth-order nonlinear difference equation \[ \Delta^2\big(p_n\,(\Delta^2y_n)^\alpha\big)+q_n\,y_{n+3}^\beta, \quad n\in{\mathbb N}. \] The main results concern the classification of positive solutions (necessary and sufficient conditions in terms of the coefficients) into one of six described classes according to their asymptotic behavior.
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nonoscillatory solution
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positive solutions
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asymptotic behavior
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classification of solutions
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oscillation
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fourth-order nonlinear difference equation
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