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On distance between zeros of solutions of third order differential equations

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Parhi N., Panigrahi S.

Annales Polonici Mathematici

2001

tom 77

nr 1

21-38

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).

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Panigrahi S.

1 Parhi N.

1 2001

Wyniki wyszukiwania

On distance between zeros of solutions of third order differential equations