comparison theorem for differential inequalities
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Comparison Theorems for Differential Equations
BASIC COMPARISON THEOREM Suppose u(t) and o(t) are continuous on the interval [a b] of the real line R and differentiable on (a b] f is a con- tinuous mapping from R x R to R and u(a) < u(a) $-fW$-f(w) on (a b] (1 1) Then u < v on [a b] Let us suppose u 2 u somewhere on [a b] |
What are comparison theorems in differential equations?
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.
Can two solutions of a differential equation intersect at singular points?
$-/(I, u), on(a, b]. andu canonly intersect at singular points where f(t, U) does not satisfy (1.2). These r sults also provide abasis forderiving upper and lower bounds for solutions of the differential equation (1.3) above.
What is a good source for obtaining comparison theorems?
One rich source for obtaining comparison theorems is the Lyapunov comparison principle with a vector function (see – ). The idea of the comparison principle is as follows. Let a system of differential equations be given, where $ v = ( v _ {1} \\dots v _ {m} ) $.
What is the application of Sturm's comparison theorem?
An important application of Sturm’s comparison theorem is in understanding zero set of non-trivial solutions of Bessel’s equation. Recall that Bessel’s equation is given by x2y′′ + xy′ + (x2 − ν2)y = 0 (ν ≥ 0). (x > 0). ✪ = v). which has a solution sin x with zeros at x = nπ, n ∈ N.
Introduction to Differential Inequalities
Comparison Properties of the Integral—Inequalities with Integrals
Comparison test for improper integrals introduction calculus 2 tutorial
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Comparison Theorems for Differential Equations
f(G 4c))=f(c v(c)). Since this violates the inequality (1.1) at c |
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A COMPARISON THEOREM OF DIFFERENTIAL EQUATIONS 1
Key words and phrases: Lipschitz condition comparison theorem. 1. Introduction. Differential inequalities are the basic tools in the qualitative theory of |
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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 stochastic differential inequalities and an
Comparison theorems for stochastic differential inequalities of ordinary and parabolic type are derived. Two methods are proposed one exploiting the. |
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A comparison theorem for differential inequalities with applications
A comparison theorem for differential inequalities with applications in quantum mechanics. To cite this article: T Hoffmann-Ostenhof 1980 J. Phys. A: Math. |
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DIFFERENTIAL INEQUALITIES
The simplest theorem on differential inequalities is the classical one we can prove that Theorem 10.1 holds true for a comparison system of. |
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Difference inequalities and comparison theorems for stability of
Comparison theorems in which the stability properties of n-dimensional systems are of Liapunov techniques and certain differential inequalities. |
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Difference inequalities and comparison theorems for stability of
Comparison theorems in which the stability properties of n-dimensional systems are of Liapunov techniques and certain differential inequalities. |
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COMPARISON THEOREMS FOR ELLIPTIC AND PARABOLIC
A recent comparison theorem of Kurt Kreith [2] will be extended to quasi- linear elliptic and parabolic differentialinequalities of second order. Ac-. |
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WIRTINGER TYPE INEQUALITIES AND ELLIPTIC DIFFERENTIAL
Nov 7 1970 type |
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Comparison Theorems for Differential Equations - CORE
119, 417428 (1986) Comparison Theorems for Differential Equations Since this violates the inequality (1 1) at c, no such c exists in [a, b] This result is our |
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Comparison Theorems for Differential Equations - ScienceDirectcom
119, 417428 (1986) Comparison Theorems for Differential Equations Since this violates the inequality (1 1) at c, no such c exists in [a, b] This result is our |
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DIFFERENTIAL INEQUALITIES
PREFACE The simplest theorem on differential inequalities is the classical one we can prove that Theorem 10 1 holds true for a comparison system of type I |
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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
Key words and phrases: Lipschitz condition, comparison theorem 1 Introduction Differential inequalities are the basic tools in the qualitative theory of dif- |
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ORDINARY DIFFERENTIAL INEQUALITIES AND
Abstract A well known comparison theorem on ordinary differential in- equalities with quasimonotone right-hand side f(t, x) was carried over by Volkmann |
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