Results 141 to 150 of about 793 (181)

A Strong Version of Liouville's Theorem

The American Mathematical Monthly, 2008
1. THE MAIN RESULT. Liouville's theorem states that every bounded holomor phic function on C is constant. Let us recall that holomorphic functions / on open subsets U of the complex plane have the mean value property, that is, for every closed disk B(z,r) in U, the value of / at its center z is equal to the average of the values of f on the circle S(z ...
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Liouville theorem for X-elliptic operators

Nonlinear Analysis: Theory, Methods & Applications, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
KOGOJ, ALESSIA ELISABETTA, Lanconelli, Ermanno   +1 more
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On Liouville’s Theorem for Biharmonic Functions

SIAM Journal on Applied Mathematics, 1971
The following theorem, called Liouville's theorem, is well known. THEOREM 1. Any harmonic function bounded either above or below in all of n-space is constant. The reader is referred to the excellent book by Protter and Weinberger [1] for the proof of the above theorem.
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A Liouville Theorem for Harmonic Maps

American Journal of Mathematics, 1995
The main result of the author is a Liouville type theorem for harmonic maps with domain \(M\), a complete Riemannian manifold of nonnegative Ricci curvature, and range \(N\), a simply-connected complete Riemannian manifold with sectional curvature bounded above by \(-a^2\), \(a>0\).
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Liouville’s theorems for Lévy operators

Mathematische Annalen
45 pages; minor ...
Tomasz Grzywny, Mateusz Kwaśnicki
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Proof of the Levinson theorem by the Sturm–Liouville theorem

Journal of Mathematical Physics, 1985
The Levinson theorem is proved by the Sturm–Liouville theorem in this paper. For the potential ∫10r‖V(r)‖dr <∞,V(r)→b/r2 when r→∞, the modified Levinson theorem is derived as nl=(1/π)δl(0) +(a−l)/2− 1/2  sin2{δl(0)+[(a−l)/2]π}, if a(a+1)≡b+l(l+1)> 3/4 or a=0.
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On the Generalized Liouville Theorem

2019
In this paper a generalization of the classical Liouville theorem for the solutions of special type elliptic systems and some nonclassical interpretations of this theorem are obtained.
Nino Manjavidze, George Makatsaria, Tamaz Vekua, George Akhalaia   +3 more
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A Note on Liouville's Theorem

The American Mathematical Monthly, 1986
(1986). A Note on Liouville's Theorem. The American Mathematical Monthly: Vol. 93, No. 3, pp. 200-201.
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A Liouville theorem on a manifold

Russian Mathematical Surveys, 1982
Translation from Usp. Mat. Nauk 37, No.3(225), 181-182 (Russian) (1982; Zbl 0509.53035).
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Phragmen-Liouville-type theorems and Liouville theorems for a linear parabolic equation

Mathematical Notes of the Academy of Sciences of the USSR, 1985
The author proves some results of Phragmén-Lindelöf type and some Liouville type theorems applying to a class of linear parabolic equations with measurable coefficients.
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