We study the semi-classical ground states of the Dirac equation with critical nonlinearity: −i~α · ∇w + aβw + V (x)w = W (x) ( g(|w|) + |w| ) w for x ∈ R3. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. We develop an argument to establish the existence of least energy solutions for ~ small. We also describe the concentration pheno...

most fetal heart rate patterns can be interpreted accurately so that management decisions can be made correctly. how-ever, few fetal heart rate patterns are so ambiguous that the obstetricians cannot interpret them precisely. a 27-year-old woman at 38 weeks' gestation in her first pregnancy was admitted with heavy vaginal bleeding and decrease in fetal movements. fetal status was indeterminate ...

The work of H. Hundal (Nonlinear Anal. 57 (2004), 35-61) has revealed that the sequence generated by the method of alternating projections converges weakly, but not strongly in general. This paper seeks to design strongly convergent algorithms by means of alternating the resolvents of two maximal monotone operators, A and B, that can be used to approximate common zeroes of A and B. In particula...

The proximal alternating direction method of multipliers (P-ADMM) is an efficient first-order method for solving the separable convex minimization problems. Recently, He et al. have further studied the P-ADMM and relaxed the proximal regularization matrix of its second subproblem to be indefinite. This is especially significant in practical applications since the indefinite proximal matrix can ...

We generalize the Morse index theorem of [12, 13] and we apply the new result to obtain lower estimates on the number of geodesics joining two fixed non conjugate points in certain classes of semi-Riemannian manifolds. More specifically, we consider semi-Riemannian manifolds (M, g) admitting a smooth distribution spanned by commuting Killing vector fields and containing a maximal negative distr...

We consider the following elliptic system:

adsorption of nh3 and h2o molecules on pristine and b–doped al12n12 nano–cage was investigated using density functional theory, by means of b3lyp and x3lyp functionals. both nh3 and h2o molecules were found to bind to an al atom of al12n12 via chemisorption, releasing energies ranging from –1.48 to –1.53 and –1.16 to –1.22 ev, respectively. the binding energies of x3lyp functional are somewhat ...

Certain properties of indefinite pronouns have received considerable attention in the literature. For instance, negative polarity indefinites such as English any constitute the focus of the bulk of the literature on negative polarity items, the fact notwithstanding that Klima in his seminal 1964 paper did not fail to show that members of other syntactic and semantic categories may be restricted...

in this paper, we investigate infinite product representation of the solution of a sturm-liouville equation with an indefinite weight function which has two zeros and/or singularitiesin a finite interval. first, by using of the asymptotic estimates provided in [w. eberhard, g.freiling, k. wilcken-stoeber, indefinite eigenvalue problems with several singular pointsand turning points, math. nachr...

In this paper, we study the following semilinear Schrödinger equation with periodic coefficient: −△u + V (x)u = f(x, u), u ∈ H1(RN). The functional corresponding to this equation possesses strongly indefinite structure. The nonlinear term f(x, t) satisfies some superlinear growth conditions and need not be odd or increasing strictly in t. Using a new variational reduction method and a generaliz...