منابع مشابه
Liouville theorems for harmonic maps
Recently there has been much interest in the Liouville type theorems for harmonic maps. For a detailed survey and progress in this direction, see the works by Hildebrandt [4], Eells and Lemaire [2]. Here we would like to mention that for all known results, the conditions on the harmonic maps can be divided into two kinds. The first of these conditions concerns the finiteness of the energy of th...
متن کاملSome Liouville theorems and applications
We give exposition of a Liouville theorem established in [6] which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the Liouville theorem, as well as that of earlier ones in [5], can be found in [6, 7] an...
متن کاملLiouville Theorems for Dirac - Harmonic Maps
We prove Liouville theorems for Dirac-harmonic maps from the Euclidean space Rn, the hyperbolic space Hn and a Riemannian manifold Sn (n ≥ 3) with the Schwarzschild metric to any Riemannian manifold N .
متن کاملLiouville-Type Theorems for Some Integral Systems
/2 ( ) ( ) u u where is the Fourier transformation and its inverse. The question is to determine for which values of the exponents pi and qi the only nonnegative solution (u, v) of (1) and (2) is trivial, i.e., (u; v) = (0, 0). When 2 , is the case of the Emden-Fowler equation 0 , 0 u u u k in N (5) When ) 3 )( 2 /( ) 2 ( 1 N N N k , it has been prove...
متن کاملSome Remarks on Liouville Type Theorems
The goal of this note is to present elementary proofs of statements related to the Liouville theorem.
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ژورنال
عنوان ژورنال: Advanced Nonlinear Studies
سال: 2020
ISSN: 2169-0375,1536-1365
DOI: 10.1515/ans-2020-2111