Displaying similar documents to “Existence of solutions for a semilinear elliptic system”

On blocks of arithmetic progressions with equal products

N. Saradha (1997)

Journal de théorie des nombres de Bordeaux

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Let f ( X ) [ X ] be a monic polynomial which is a power of a polynomial g ( X ) [ X ] of degree μ 2 and having simple real roots. For given positive integers d 1 , d 2 , , m with < m and gcd ( , m ) = 1 with μ m + 1 whenever m < 2 , we show that the equation f ( x ) f ( x + d 1 ) f ( x + ( k - 1 ) d 1 ) = f ( y ) f ( y + d 2 ) f ( y + ( m k - 1 ) d 2 ) with f ( x + j d 1 ) 0 for 0 j < k has only finitely many solutions in integers x , y and k 1 except in the case m = μ = 2 , = k = d 2 = 1 , f ( X ) = g ( X ) , x = f ( y ) + y .

The new properties of the theta functions

Stefan Czekalski (2013)

Annales mathématiques Blaise Pascal

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It is shown, that the function H ( x ) = k = - e - k 2 x satisfies the relation H ( x ) = n = 0 ( 2 π ) 2 n ( 2 n ) ! H ( n ) ( x ) .

Differential equations on the plane with given solutions.

R. Ramírez, N. Sadovskaia (1996)

Collectanea Mathematica

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The aim of this paper is to construct the analytic vector fields with given as trajectories or solutions. In particular we construct the polynomial vector field from given conics (ellipses, hyperbola, parabola, straight lines) and determine the differential equations from a finite number of solutions.

Non-free two-generator subgroups of SL(Q).

S. Peter Farbman (1995)

Publicacions Matemàtiques

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The question of whether two parabolic elements A, B of SL(C) are a free basis for the group they generate is considered. Some known results are generalized, using the parameter τ = tr(AB) - 2. If τ = a/b ∈ Q, |τ| < 4, and |a| ≤ 16, then the group is not free. If the subgroup generated by b in Z / aZ has a set of representatives, each of which divides one of b ± 1, then the subgroup of SL(C) will not be free.

Topological properties of two-dimensional number systems

Shigeki Akiyama, Jörg M. Thuswaldner (2000)

Journal de théorie des nombres de Bordeaux

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In the two dimensional real vector space 2 one can define analogs of the well-known q -adic number systems. In these number systems a matrix M plays the role of the base number q . In the present paper we study the so-called fundamental domain of such number systems. This is the set of all elements of 2 having zero integer part in their “ M -adic” representation. It was proved by Kátai and Környei, that is a compact set and certain translates of it form a tiling of the 2 . We construct...