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Journal ArticleDOI

On the non-existence of conjugate points.*

Aurel Wintner
- 01 Apr 1951 - 
- Vol. 73, Iss: 2, pp 368
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This article is published in American Journal of Mathematics.The article was published on 1951-04-01. It has received 183 citations till now. The article focuses on the topics: Conjugate points & Conjugate element.

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Bessel pairs and optimal Hardy and Hardy–Rellich inequalities

Nassif Ghoussoub, +1 more
- 01 Jan 2011 - 
TL;DR: In this paper, the authors give necessary and sufficient conditions on a pair of positive radial functions V and W on a ball B of radius R in R to obtain the following inequalities.
Book

Functional Inequalities: New Perspectives and New Applications

Nassif Ghoussoub, +1 more
TL;DR: Hardy type inequalities: Bessel pairs and Sturm's oscillation theory The classical Hardy inequality and its improvements Improved Hardy inequality with boundary singularity Weighted Hardy inequalities The Hardy inequalities and second order nonlinear eigenvalue problems Hardy-Rellich type inequalities.
Journal ArticleDOI

Curvature Functions for Open 2-Manifolds

Jerry L. Kazdan, +1 more
- 01 Mar 1974 - 
TL;DR: For non-compact 2-manifolds, the problem of describing the set of Gaussian curvature functions which a given 2-dimensional manifold M can possess has been studied in this paper.
Journal ArticleDOI

Oscillation criteria for half-linear dynamic equations on time scales

Taher S. Hassan
- 01 Sep 2008 - 
TL;DR: In this article, the second-order half-linear delay dynamic equation (r(t)(x � )) � + p(t)x(τ(t)) = 0, on a time scale T, where γ ≥ 1 is the quotient of odd positive integers, p( t), and τ : T → T are positive rd-continuous functions on T, r(t), ρ is positive and (delta) differentiable, τ (t) ≤ t, and limt→∞ τ(τ) = ∞.
Journal ArticleDOI

Lyapunov-type integral inequalities for certain higher order differential equations

Devrim Çakmak
- 01 Mar 2010 - 
TL;DR: First a short survey of the most basic results on Lyapunov inequality is given, and next this-type integral inequalities for certain higher order differential equations are obtained.