On the number of solutions to systems of Pell equations
β Scribed by Mihai Cipu; Maurice Mignotte
- Publisher
- Elsevier Science
- Year
- 2007
- Tongue
- English
- Weight
- 292 KB
- Volume
- 125
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
In this paper we consider the following n-dimensional second-order nonlinear system on time scales f i (u)/ u . Define i 0 = number of zeros in the set {f 0 , f β } and i β = number of infinities in the set {f 0 , f β }. By using fixed point index theory, we show that: (i) if i 0 = 1 or 2, then th
We consider systems of homogenous polynomial equations of degree d in a projective space β«ήβ¬ m over a finite field β«ήβ¬ q . We attempt to determine the maximum possible number of solutions of such systems. The complete answer for the case r Ο 2, d Ο½ q Οͺ 1 is given, as well as new conjectures about th
We count the number of solutions with height less than or equal to \(B\) to a system of linear equations over a number field. We give explicit asymptotic estimates for the number of such solutions as \(B\) goes to infinity, where the constants involved depend on the classical invariants of the numbe
## Abstract We consider a suitable weak solution to the threeβdimensional NavierβStokes equations in the spaceβtime cylinder Ξ© Γ ]0, __T__[. Let Ξ£ be the set of singular points for this solution and Ξ£ (__t__) β‘ {(__x, t__) β Ξ£}. For a given open subset Ο β Ξ© and for a given moment of time __t__ β]0
## Abstract The paper deals with the existence, multiplicity and nonexistence of positive radial solutions for the elliptic system div(|β|^__p__ β2^β) + __Ξ»k~i~__ (|__x__ |) __f^i^__ (__u__~1~, β¦,__u~n~__) = 0, __p__ > 1, __R__~1~ < |__x__ | < __R__~2~, __u~i~__ (__x__) = 0, on |__x__ | = __R__~1~