Disfocality and Liapunov-type inequalities for third-order equations

✍ Scribed by N Parhi; S Panigrahi

• Book ID: 104349530
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 319 KB
• Volume: 16
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(03)80036-8

✦ Synopsis

The concept of disfocality is introduced for third-order differential equations y"' + p(t)y = O. (*) This helps to improve the Liapunov inequality when y(t) is a solution of (*) with y(a) = 0 = y~(a), y(b) = 0 = y'(b), and y(t) ¢ 0, t • (a, b). If y(t) is a solution of (*) with y(tl) = 0 = y(t2) = y(t3) = y(t4) (tl < t2 < ta < t4) and y(t) ¢ 0 for t • U~=l(ti,ti+l), then the lower bound for (t4 -tl) is obtained. A new criteria is obtained for disconjugacy of (*) in [a, b].