Oscillation of Second-Order Sublinear Impulsive Differential Equations
Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type: x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0, t≠θk; Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0; Δx(t)|t=θk=0, (0<...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/458275 |
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| author | A. Zafer |
| author_facet | A. Zafer |
| author_sort | A. Zafer |
| collection | DOAJ |
| description | Oscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type:
x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0, t≠θk; Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0; Δx(t)|t=θk=0, (0<α<1) by considering the cases τ(t)≤t and τ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions. |
| format | Article |
| id | doaj-art-d365b5106a5d435cb8796214ae98d8f5 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d365b5106a5d435cb8796214ae98d8f52025-02-03T01:29:08ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/458275458275Oscillation of Second-Order Sublinear Impulsive Differential EquationsA. Zafer0Department of Mathematics, Middle East Technical University, 06800 Ankara, TurkeyOscillation criteria obtained by Kusano and Onose (1973) and by Belohorec (1969) are extended to second-order sublinear impulsive differential equations of Emden-Fowler type: x″(t)+p(t)|x(τ(t))|α-1x(τ(t))=0, t≠θk; Δx'(t)|t=θk+qk|x(τ(θk))|α-1x(τ(θk))=0; Δx(t)|t=θk=0, (0<α<1) by considering the cases τ(t)≤t and τ(t)=t, respectively. Examples are inserted to show how impulsive perturbations greatly affect the oscillation behavior of the solutions.http://dx.doi.org/10.1155/2011/458275 |
| spellingShingle | A. Zafer Oscillation of Second-Order Sublinear Impulsive Differential Equations Abstract and Applied Analysis |
| title | Oscillation of Second-Order Sublinear Impulsive Differential Equations |
| title_full | Oscillation of Second-Order Sublinear Impulsive Differential Equations |
| title_fullStr | Oscillation of Second-Order Sublinear Impulsive Differential Equations |
| title_full_unstemmed | Oscillation of Second-Order Sublinear Impulsive Differential Equations |
| title_short | Oscillation of Second-Order Sublinear Impulsive Differential Equations |
| title_sort | oscillation of second order sublinear impulsive differential equations |
| url | http://dx.doi.org/10.1155/2011/458275 |
| work_keys_str_mv | AT azafer oscillationofsecondordersublinearimpulsivedifferentialequations |