On distance between zeros of solutions of third order differential equations

• Autorzy: N. Parhi , S. Panigrahi
• Języki publikacji: EN

Abstrakty

EN

The lower bounds of the spacings b-a or a'-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form
y''' + q(t)y' + p(t)y = 0 (*)
are derived under very general assumptions on p and q. These results are then used to show that $t_{n+1} - tₙ → ∞$ or $t_{n+2} - tₙ → ∞$ as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a or b-d for a solution y(t) of (*) with y(a) = 0 = y'(a), y'(c) = 0 and y''(d) = 0 where d ∈ (a,c) or y'(c) = 0, y(b) = 0 = y'(b) and y''(d) = 0 where d ∈ (c,b).

Kategorie tematyczne

• 34C10: Oscillation theory, zeros, disconjugacy and comparison theory
• 34C15: Nonlinear oscillations, coupled oscillators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2001
• Tom: 77
• Numer: 1
• Strony: 21-38

Daty

wydano

2001

Twórcy

autor

N. Parhi

• Department of Mathematics, Berhampur University, Berhampur 760007, India

autor

S. Panigrahi

• Department of Mathematics, Berhampur University, Berhampur 760007, India

Identyfikatory

DOI

10.4064/ap77-1-3