Results 21 to 30 of about 94 (85)
Sturmian comparison theorems for three-term recurrence equations
Journal of Mathematical Analysis and Applications, 1985 The author considers a discrete analogue of an ordinary, regular, self- adjoint second-order differential equation. For these homogeneous difference equations (or recurrences) with homogeneous discrete boundary conditions of Sturm-Liouville type, several comparison theorems concerning the existence and inclusion of nodes of the corresponding non ...
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International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We obtain the asymptotic distribution of the nonprincipal eigenvalues associated with the singular problem x″ + λq(t)x = 0 on an infinite interval [a, +∞). Similar to the regular eigenvalue problem on compact intervals, we can prove a Weyl‐type expansion of the eigenvalue counting function, and we derive the asymptotic behavior of the eigenvalues.
Juan Pablo Pinasco
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A Sturm theorem for partial differential equations of mixed type
, 1981 A generalization of the Sturm comparison theorem is given for differential equations of mixed type. The results constitute a generalization of Sturmian theorems used in the study of hyperbolic initial boundary value problems.
Kurt Kreith
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Symplectic difference systems: oscillation theory and hyperbolic Prüfer transformation
Abstract and Applied Analysis, Volume 2004, Issue 4, Page 285-294, 2004., 2004 We present basic methods of oscillation theory of symplectic difference systems (SDSs). A particular attention is devoted to the variational principle and to the transformation method. Hyperbolic Prüfer transformation for SDSs is established.
Ondřej Došlý
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, 1980 SynopsisThe oscillatory behaviour of quasilinear hyperbolic equations of the formis studied using a Sturmian-type comparison theorem. We assume that for some function ψ′(x)≦0 and ψ′(x≦0.) The existence of the first nodal line of u is then inferred from
Man Kam Kwong, Wu-Teh Hsiang
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On certain comparison theorems for half‐linear dynamic equations on time scales
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 551-565, 2004., 2004 We obtain comparison theorems for the second‐order half‐linear dynamic equation [r(t)Φ(yΔ)]Δ+p(t)Φ(yσ)=0, where Φ(x) = |x|α−1sgn x with α > 1. In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient p(t) by a suitable function q(t) and lower the exponent α in the nonlinearity Φ ...
Pavel Řehák
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On the zeroes and the critical points of a solution of a second order half-linear differential equation [PDF]
, 2012 This paper presents two methods to obtain upper bounds for the distance between a zero and an adjacent critical point of a solution of the second-order half-linear di¿erential equation p x ¿ y q x ¿ y 0, with p x and q x piecewise ...
Lucas Jódar +3 more
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Substitutions and their Generalisations
Israel Journal of Chemistry, Volume 64, Issue 10-11, November 2024.Abstract Tilings and point sets arising from substitutions are classical mathematical models of quasicrystals. Their hierarchical structure allows one to obtain concrete answers regarding spectral questions tied to the underlying measures and potentials.
Neil Mañibo
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On polynomials of Sheffer type arising from a Cauchy problem
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 33, Page 2119-2137, 2003., 2003 A new sequence of eigenfunctions is developed and studied in depth. These theta polynomials are derived from a recent analytic solution of the canonical Cauchy problem for parabolic equations, namely, the inverse heat conduction problem. By appealing to the methods of the operator calculus, it is possible to categorize the new functions as polynomials ...
D. G. Meredith
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Picone's identity for a Finsler $p$-Laplacian and comparison of nonlinear elliptic equations [PDF]
, 2014 summary:In the paper we present an identity of the Picone type for a class of nonlinear differential operators of the second order involving an arbitrary norm $H$ in $\mathbb {R}^n$ which is continuously differentiable for $x \not = 0$ and such that $H^p$
Jaroš, Jaroslav
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