Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space

The first author is partially supported by a GENIL grant YTR-2011-7 (Spain) and by the grant PN-II-RU-TE-2011-3-0157 (Romania). The second author is partially supported by the grant PN-II-RU-TE-2011-3-0157 (Romania). The third author is partially supported by Ministerio de Economia y Competitividad, Spain, project MTM2011-23652.In this paper, by using Leray-Schauder degree arguments and critical point theory for convex, lower semicontinuous perturbations of C1-functionals, we obtain existence of classical positive radial solutions for Dirichlet problems of type div ( √1 − |∇ ∇v v|2 ) + f(|x|; v) = 0 in B(R); v = 0 on @B(R): Here, B(R) = {x ∈ RN : |x| < R} and f : [0; R] × [0; α) → R is a continuous function, which is positive on (0; R] × (0; α):GENIL (Spain) YTR-2011-7Ministerio de Economia y Competitividad, Spain MTM2011-23652PN-II-RU-TE-2011-3-015

Cofactorization on Graphics Processing Units

We show how the cofactorization step, a compute-intensive part of the relation collection phase of the number field sieve (NFS), can be farmed out to a graphics processing unit. Our implementation on a GTX 580 GPU, which is integrated with a state-of-the-art NFS implementation, can serve as a cryptanalytic co-processor for several Intel i7-3770K quad-core CPUs simultaneously. This allows those processors to focus on the memory-intensive sieving and results in more useful NFS-relations found in less time

Periodic solutions of singular nonlinear perturbations of the ordinary p-Laplacian

Using some recent extensions of upper and lower solutions techniques and continuation theorems to the periodic solutions of quasilinear equations of p-Laplacian type, we prove the existence of positive periodic solutions of equations of the form (x'(p-2)x')' + f(x)x' + g(x) = h(t) with p > 1, f arbitrary and g singular at 0. This extends results of Lazer and Solimini for the undamped ordinary differential case

On noncoercive periodic systems with vector p-Laplacian

We consider nonlinear periodic systems driven by the vector $p$-Laplacian. An existence and a multiplicity theorem are proved. In the existence theorem the potential function is $p$-superlinear, but in general does not satisfy the AR-condition. In the multiplicity theorem the problem is strongly resonant with respect to the principal eigenvalue $\lambda_0=0$. In both of the cases the Euler-Lagrange functional is noncoercive and the method is variational

Morse theory and multiple periodic solutions of some quasilinear difference systems with periodic nonlinearities

We consider the system of difference equations Δ ( Δ un - 1 1 - | Δ un - 1 | 2 ) = ∇ Vn ( un ) + h n , un = un + T ( n ∈ ℤ ) , with Δ un = un + 1 - un ∈ ℝ N, Vn = Vn ( x ) ∈ C 2 ( ℝ N , ℝ ), Vn + T = Vn, h n + T = h n for all n ∈ ℤ and some positive integer T, Vn ( x ) is ω i-periodic ( ω i > 0) with respect to each x i ( i = 1 , ... , N) and ∑ j = 1 T h j = 0. Applying a modification argument to the corresponding problem with a left-hand member of p-Laplacian type, and using Morse theory, we prove that if all its solutions are non-degenerate, then the difference system above has at least 2 N geometrically distinct T-periodic solutions

Radial solutions for some nonlinear problems involving mean curvature operators in Euclidean and Minkowski spaces

In this paper, using the Schauder fixed point theorem, we prove existence results of radial solutions for Dirichlet problems in the unit ball and in an annular domain, associated to mean curvature operators in Euclidean and Minkowski spaces