comparison theorem differential equations
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Comparison Theorems for Differential Equations
INTRODUCTION This note isconcerned with extensions of the following: BASICCOMPARISON THEOREM Suppose u(t) and o(t) are continuous on the interval [a b] of the real line Rand ifferentiable on (a b] fis a con- tinuous mapping from R xR toR and u(a) < u(a) $-fW$-f(w) on(a b] (1 1) Thenu< von [a b] Letus suppose u 2 u somewhere on [a b] |
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A comparison theorem of differential equations
Abstract In this paper it is proved that for comparing the solutions of two differential equations it is enough that one of them is unique; i e no |
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Chapter 7 Sturms Separation and Comparison theorems
Theorem 7 6 (Comparison) Let φ1 and φ2 be non-trivial solutions of equations y′′ + q1(x)y = 0 MA 417: Ordinary Differential Equations Sivaji Ganesh Sista |
What is the statement of Sturm comparison theorem?
and conclude that between any two consecutive zeros, α and β of v, there exists at least one zero of sinx.
Thus, we have α<nπ<β for some n ∈ N.
Remark 7.13 (i) Sturm's comparison theorem guarantees the existence of at least one zero. (ii) The assumption q2(x) ≥ q1(x) can not be dropped.What is the comparison principle?
A nonlinear elliptic partial differential equation with the New- ton boundary conditions is examined.
We prove that for greater data we get a greater weak solution.
This is the so-called comparison principle.
It is applied to a steady-state heat conduction problem in anisotropic magnetic cores of large transformers.What is the comparison theory in math?
In the theory of differential equations, comparison theorems assert particular properties of solutions of a differential equation (or of a system thereof), provided that an auxiliary equation/inequality (or a system thereof) possesses a certain property.
Types of Differential Equations
Types of Differential Equations
Ordinary Differential Equations.Partial Differential Equations.Linear Differential Equations.Nonlinear differential equations.Homogeneous Differential Equations.Nonhomogeneous Differential Equations.
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Separable First Order Differential Equations
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Comparison Theorems for Differential Equations
Comparison Theorems for Differential Equations. A. MCNABB This result is our prototype weak comparison theorem. Iff(t U) satisfies a Lipschitz ... |
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A COMPARISON THEOREM OF DIFFERENTIAL EQUATIONS 1
1 2010 |
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Comparison Theorems for Linear Differential Equations of Second
COMPARISON THEOREMS FOR LINEAR DIFFERENTIAL. EQUATIONS OF SECOND ORDER. WALTER LEIGHTON'. 1. In this paper we consider self-adjoint differential equations |
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A COMPARISON THEOREM FOR SOLUTIONS OF STOCHASTIC
OF STOCHASTIC DIFFERENTIAL EQUATIONS. AND ITS APPLICATIONS. NOBUYUKI IKEDA AND SHINZO WATANABE. (Received August 2 1976). Introduction. Comparison theorem |
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A Comparison Theorem for Solutions of Stochastic Differential
In the investigation of solutions of stochastic differential equations (SDEs) com- parison theorems are very powerful tools as in the case for |
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A COMPARISON THEOREM FOR SOLUTIONS OF STOCHASTIC
OF STOCHASTIC DIFFERENTIAL EQUATIONS. AND ITS APPLICATIONS. NOBUYUKI IKEDA AND SHINZO WATANABE. (Received August 2 1976). Introduction. Comparison theorem |
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A Comparison Theorem For Self-Adjoint Differential Equations of
theorem for the ordinary linear differential equations property involved is actually a comparison theorem on focal points as pre- sented in Section 2. |
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A GENERAL COMPARISON THEOREM FOR BACKWARD
Keywords: BSDE; comparison theorem; nonlinear expectation; dynamic risk measure The theory of backward stochastic differential equations (BSDEs) is an ... |
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Sturm-Picone Comparison Theorem of Second-Order Linear
Sturm-Picone Comparison Theorem of. Second-Order Linear Equations on Time Scales. Chao Zhang and Shurong Sun. School of Science University of Jinan |
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Comparison principles for fractional differential equations with the
Now we present a comparison principle for fractional differential equation with the. Caputo derivative under strict inequalities when p ? (0 |
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Comparison Theorems for Differential Equations - CORE
Comparison Theorems for Differential Equations This result is our prototype weak comparison theorem solutions of the differential equation (1 3) above |
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Comparison Theorems for Differential Equations - ScienceDirectcom
Comparison Theorems for Differential Equations This result is our prototype weak comparison theorem solutions of the differential equation (1 3) above |
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A COMPARISON THEOREM OF DIFFERENTIAL EQUATIONS 1
In this paper it is proved that for comparing the solutions of two differential equations it is enough that one of them is unique; i e no Lipschitz condition is needed Differential inequalities are the basic tools in the qualitative theory of dif- ferential equations |
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A COMPARISON THEOREM OF DIFFERENTIAL EQUATIONS 1
In this paper it is proved that for comparing the solutions of two differential equations it is enough that one of them is unique; i e no Lipschitz condition is needed Differential inequalities are the basic tools in the qualitative theory of dif- ferential equations |
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Comparison Theorems for Linear Differential Equations of - JSTOR
COMPARISON THEOREMS FOR LINEAR DIFFERENTIAL EQUATIONS OF SECOND ORDER WALTER LEIGHTON' 1 In this paper we consider self-adjoint |
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Comparison Theorems for Homogeneous Linear - JSTOR
associated with adjoint linear differential equations of order n, first defined in classical theorem of comparison for linear homogeneous binomial equa- tions of |
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COMPARISON THEOREMS FOR SECOND ORDER DIFFERENTIAL
In order to prove the sufficiency, we require the following lemma Lemma 1 The matrix Riccati equation (MR) has a unique solution S on J = [ft, T)(ft)) |
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STURM COMPARISON THEOREMS FOR ORDINARY AND
Picone [7]) 2 Ordinary differential equations In seeking to prove a "Sturm comparison theorem, for a single equation or a system of equations, |
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DIFFERENTIAL INEQUALITIES
Some notions and theorems on ordinary differential equations Let the right-hand we can prove that Theorem 10 1 holds true for a comparison system of type I |
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