On the Zeros of Functions in the Bers Space
A. Fletcher, V. Marković (2004)
Publications de l'Institut Mathématique
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A. Fletcher, V. Marković (2004)
Publications de l'Institut Mathématique
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M. Z. Garaev (2003)
Acta Arithmetica
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Chantladze, T., Kandelaki, N., Lomtatidze, A. (1999)
Memoirs on Differential Equations and Mathematical Physics
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J. Knežević-Miljanović (1992)
Matematički Vesnik
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N. Parhi, S. Panigrahi (2001)
Annales Polonici Mathematici
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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 or 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...
K. Srinivas (2002)
Acta Arithmetica
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Lopes-Pinto, António J.B. (1998)
Journal of Convex Analysis
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Yūki Naito (2011)
Mathematica Bohemica
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We consider the boundary value problem involving the one dimensional -Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.