Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations
The authors consider the mth order nonlinear difference equations of the form Dmyn+qnf(yσ(n))=ei, where m≥1, n∈ℕ={0,1,2,…}, ani>0 for i=1,2,…,m−1, anm≡1, D0yn=yn, Diyn=aniΔDi−1yn, i=1,2,…,m, σ(n)→∞ as n→∞, and f:ℝ→ℝ is continuous with uf(u)>0 for u≠0. They give sufficient conditions to ensure...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006172 |
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| author | E. Thandapani S. Lourdu Marian John R. Graef |
| author_facet | E. Thandapani S. Lourdu Marian John R. Graef |
| author_sort | E. Thandapani |
| collection | DOAJ |
| description | The authors consider the mth order nonlinear difference
equations of the form Dmyn+qnf(yσ(n))=ei, where
m≥1, n∈ℕ={0,1,2,…}, ani>0 for
i=1,2,…,m−1, anm≡1, D0yn=yn, Diyn=aniΔDi−1yn, i=1,2,…,m, σ(n)→∞ as n→∞, and f:ℝ→ℝ is continuous with uf(u)>0 for u≠0. They give sufficient conditions to
ensure that all bounded nonoscillatory solutions tend to zero as
n→∞ without assuming that ∑n=0∞1/ani=∞, i=1,2,…,m−1, {qn} is positive, or en≡0 as is often required. If {qn} is positive, they prove another such result for all
nonoscillatory solutions. |
| format | Article |
| id | doaj-art-694f04f793ae467190dbb28f17598d46 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-694f04f793ae467190dbb28f17598d462025-02-03T01:22:15ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01272697610.1155/S0161171201006172Asymptotic decay of nonoscillatory solutions of general nonlinear difference equationsE. Thandapani0S. Lourdu Marian1John R. Graef2Department of Mathematics, Periyar University, Salem 636011, Tamil Nadu, IndiaDepartment of Mathematics, Periyar University, Salem 636011, Tamil Nadu, IndiaDepartment of Mathematics, University of Tennessee at Chattanooga, Chattanooga 37403, TN, USAThe authors consider the mth order nonlinear difference equations of the form Dmyn+qnf(yσ(n))=ei, where m≥1, n∈ℕ={0,1,2,…}, ani>0 for i=1,2,…,m−1, anm≡1, D0yn=yn, Diyn=aniΔDi−1yn, i=1,2,…,m, σ(n)→∞ as n→∞, and f:ℝ→ℝ is continuous with uf(u)>0 for u≠0. They give sufficient conditions to ensure that all bounded nonoscillatory solutions tend to zero as n→∞ without assuming that ∑n=0∞1/ani=∞, i=1,2,…,m−1, {qn} is positive, or en≡0 as is often required. If {qn} is positive, they prove another such result for all nonoscillatory solutions.http://dx.doi.org/10.1155/S0161171201006172 |
| spellingShingle | E. Thandapani S. Lourdu Marian John R. Graef Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations International Journal of Mathematics and Mathematical Sciences |
| title | Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations |
| title_full | Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations |
| title_fullStr | Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations |
| title_full_unstemmed | Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations |
| title_short | Asymptotic decay of nonoscillatory solutions of general nonlinear difference equations |
| title_sort | asymptotic decay of nonoscillatory solutions of general nonlinear difference equations |
| url | http://dx.doi.org/10.1155/S0161171201006172 |
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