Displaying similar documents to “Zeros of derivatives of solutions to singular ( p , n - p ) conjugate BVPs”

On distance between zeros of solutions of third order differential equations

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 t n + 1 - t or t n + 2 - t 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...

Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional p -Laplacian

Yūki Naito (2011)

Mathematica Bohemica

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We consider the boundary value problem involving the one dimensional p -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.