Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4618342 | Journal of Mathematical Analysis and Applications | 2011 | 15 Pages |
Abstract
In this paper, by arithmetic-geometric mean inequality and Riccati transformation, interval oscillation criteria are established for second-order forced impulsive differential equation with mixed nonlinearities of the form{(r(t)Φα(xâ²(t)))â²+p0(t)Φα(x(t))+âi=1npi(t)Φβi(x(t))=e(t),tâ Ïk,x(Ïk+)=akx(Ïk),xâ²(Ïk+)=bkxâ²(Ïk), where t⩾t0, kâN; Φâ(u)=|u|ââ1u; {Ïk} is the impulse moments sequence with 0⩽t0=Ï0<Ï1<Ï2<â¯<Ïk<⯠and limkââÏk=â; α=p/q, p, q are odds, and the exponents satisfyβ1>â¯>βm>α>βm+1>â¯>βn>0. Some known results are generalized and improved. Examples are also given to illustrate the effectiveness and non-emptiness of our results.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zhonghai Guo, Xiaoliang Zhou, Weigao Ge,