International audienceIn this paper we consider the problem of finding periodic solutions of certain Euler-Lagrange equations. We employ the direct method of the calculus of variations, i.e. we obtain solutions minimizing certain functional I. We give conditions which ensure that I is finitely defined and differentiable on certain subsets of Orlicz-Sobolev spaces W 1 L Φ associated to an N-function Φ. We show that, in some sense, it is necessary for the coercitivity that the complementary function of Φ satisfy the ∆ 2-condition. We conclude by discussing conditions for the existence of minima of I
This article presents a variation of the integral transform method to evaluate multicenter bielectronic integrals (12͉34), with 1s Slater-type orbitals. It is proved that it is possible to define, out of the expression of (12͉34) given by the integral transform method, a function F(q) that has the property of having a unique Q, such that F(Q) ϭ (12͉34). Therefore, F(q) may be used to calculate (12͉34). It is shown that the evaluation of F(Q) turns out to be simpler than the three-dimensional integral involved in the calculation of (12͉34), and an algorithm is presented to calculate Q. The results show that relative errors on the order of 10 Ϫ3 or lower are obtained very efficiently. In addition, it is shown that the proposed algorithm is very stable.
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AN OPTIMIZATION PROBLEM FOR NONLINEAR STEKLOV EIGENVALUES WITH A BOUNDARY POTENTIALJULIÁN FERNÁNDEZ BONDER, GRACIELA O. GIUBERGIA, AND FERNANDO D. MAZZONE Abstract.In this paper, we analyze an optimization problem for the first (nonlinear) Steklov eigenvalue plus a boundary potential with respect to the potential function which is assumed to be uniformly bounded and with fixed L 1 -norm.
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