Results 11 to 20 of about 74,153 (309)
Proceedings of the American Mathematical Society, 1976 A general comparison theorem is extracted from the proof of a recent comparison theorem of Leighton and Oo Kian Ke. The result is applied to a comparison theorem for focal points.
H. Guggenheimer
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Journal of Differential Equations, 1978 AbstractThis paper gives a generalization of the Sturm comparison theorem for differential equations (p): y″ = p(t)y, (q): y″ = q(t)y under the assumption that the function p − q changes its sign exactly once on [a, b] or ∝tbp − q, ∝atp − q maintain the sign on [a, b].
Staněk, Svatoslav
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A new look at an old comparison theorem [PDF]
, 2021 summary:We present an integral comparison theorem which guarantees the global existence of a solution of the generalized Riccati equation on the given interval $[a,b)$ when it is known that certain majorant Riccati equation has a global solution on $[a,b)
Jaroš, Jaroslav
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Electronic Journal of Qualitative Theory of Differential Equations, 2011 The theory of $u_{0}$-positive operators with respect to a cone in a Banach space is applied to the linear differential equations $u^{(4)}+\lambda_{1} p(x)u=0$ and $u^{(4)}+\lambda_{2} q(x)u=0$, $0\leq x\leq 1$, with each satisfying the boundary ...
Jeffrey Neugebauer
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A Note on Comparison Theorems [PDF]
Proceedings of the American Mathematical Society, 1977 Comparison theorems for solutions, for focal points and conjugate points of second order linear differential equations are given in this paper.
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Comparison theorem for oscillation of fourth-order nonlinear retarded dynamic equations
Electronic Journal of Qualitative Theory of Differential Equations, 2013 This work is concerned with oscillation of a class of fourth-order nonlinear delay dynamic equations on a time scale. A new comparison theorem is established that improves related results reported in the literature.
Chenghui Zhang +2 more
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Entropy, 2021 With the development of wireless sensor networks (WSNs), energy constraints and network security have become the main problems. This paper discusses the dynamic of the Susceptible, Infected, Low-energy, Susceptible model under pulse charging (SILS-P) in ...
Guiyun Liu +5 more
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A Comparison Theorem for Eigenfunctions [PDF]
Proceedings of the American Mathematical Society, 1973 A comparison theorem of Sturm's type is obtained for eigenfunctions of general linear elliptic partial differential operators of second order on bounded domains of n-dimensional Euclidean space. The proof is almost immediate from an earlier identity of the author. The theorem is shown to be stronger than some recent theorems of Kurt Kreith.
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On Leighton's comparison theorem
Journal of Differential Equations, 2017 We give a simple proof of a fairly flexible comparison theorem for equations of the type $-(p(u'+su))'+rp(u'+su)+qu=0$ on a finite interval where $1/p$, $r$, $s$, and $q$ are real and integrable. Flexibility is provided by two functions which may be chosen freely (within limits) according to the situation at hand.
Ghatasheh, Ahmed, Weikard, Rudi
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