Results 251 to 260 of about 646,050 (293)
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1994
A proof of the following theorem is given: The equation \((k-1)! (p-k)!+ (-1)^{k+1} =p^ m\) has no solution in primes \(p>7\) and natural numbers \(m\) and \(k\) with \(1\leq k\leq p\).
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A proof of the following theorem is given: The equation \((k-1)! (p-k)!+ (-1)^{k+1} =p^ m\) has no solution in primes \(p>7\) and natural numbers \(m\) and \(k\) with \(1\leq k\leq p\).
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A generalization of the Liouville–Arnol'd theorem
Mathematical Proceedings of the Cambridge Philosophical Society, 1995AbstractWe show that the Liouville-Arnol'd theorem concerning knowledge of involutory first integrals for Hamiltonian systems is available for any system of second order ordinary differential equations. In establishing this result we also provide a new proof of the standard theorem in the setting of non-autonomous, regular Lagrangian mechanics on the ...
J. Sherring +3 more
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Archive for Rational Mechanics and Analysis, 2013
We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori ...
Alexandre Montaru +2 more
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We study qualitative properties of positive solutions of noncooperative, possibly nonvariational, elliptic systems. We obtain new classification and Liouville type theorems in the whole Euclidean space, as well as in half-spaces, and deduce a priori ...
Alexandre Montaru +2 more
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A Strong Version of Liouville's Theorem
The American Mathematical Monthly, 20081. 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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A Liouville theorem for the viscous Burgers’s equation
Journal d'Analyse Mathématique, 2002The authors' classify a class of bounded entire solutions to the viscous Burgers equation. The main result is: under an extra very weak integrability condition in space, at a single time, only the travelling waves exist.
Frank Merle +2 more
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On Liouville’s Theorem for Biharmonic Functions
SIAM Journal on Applied Mathematics, 1971The 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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On the Generalized Liouville Theorem
2019In 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.
Tamaz Vekua +3 more
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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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(1986). A Note on Liouville's Theorem. The American Mathematical Monthly: Vol. 93, No. 3, pp. 200-201.
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An extension of liouville's theorem
1979I . Motivation, Computing integrals h0s been a favorite pastime of algebraic manipulators (bol, h human and machine) for some time. The usual problem is to determine if the integral of a function can be expressed in terms of some prespecitled set of functions.
Richard Zippel, Joel Moses
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A Liouville Theorem for Harmonic Maps
American Journal of Mathematics, 1995The 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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