By means of a variational identity of Pohožaev-Pucci-Serrin type for solutions of class C recently obtained, we give some necessary conditions for locating the concentration points for a class of quasi-linear elliptic problems in divergence form. More precisely we show that the points where the concentration occurs must be critical, either in a generalized or in the classical sense, for a suita...

Phenomenological evidence and analytic approximations to the QCD ground state suggest a complex gluon condensate structure. Exclusion of elementary fermion excitations by the generation of infinite mass corrections is a consequence. In addition the existence of vacuum condensates in unbroken non-abelian gauge theories, endows SU(3) and higher order groups with a non-trivial structure in the man...

We present a method for modeling disordered solid solutions, based on the virtual crystal approximation ~VCA!. The VCA is a tractable way of studying configurationally disordered systems; traditionally, the potentials which represent atoms of two or more elements are averaged into a composite atomic potential. We have overcome significant shortcomings of the standard VCA by developing a potenti...

We consider the three dimensional gravitational Vlasov-Poisson (GVP) system in both classical and relativistic cases. The classical problem is subcritical in the natural energy space and the stability of a large class of ground states has been derived by various authors. The relativistic problem is critical and displays finite time blow up solutions. Using standard concentration compactness tec...

has been studied by several authors, where 1 < p for N = 2, 1 < p < (N + 2)/(N − 2) for N ≥ 3 and Q(x) is a positive bounded continuous function. If Q(x) is a radial function, we can find infinity many solutions of problem (PQ) by restricting our attention to the radial functions (cf. [2, 5]). IfQ(x) is nonradial, we encounter a difficulty caused by the lack of a compact embedding of Sobolev ty...

which arises in various physical contexts as a model for the interaction of long and short nonlinear waves. Ground states of the system are, by definition, minimizers of the energy functional subject to constraints on conserved functionals associated with symmetries of the system. In particular, ground states have a simple time dependence because they propagate via those symmetries. For a range...

The aim of this paper is to study radial symmetry properties for ground state solutions of elliptic equations involving a regional fractional Laplacian, namely (−∆)ρ u+ u = f(u) in R, for α ∈ (0, 1). (1) In [9], the authors proved that problem (1) has a ground state solution. In this work we prove that the ground state level is achieved by a radially symmetry solution. The proof is carried out ...

We study the asymptotic behavior of solutions to the nonlocal nonlinear equation (−∆p) u = |u|u in a bounded domain Ω ⊂ R as q approaches the critical Sobolev exponent p∗ = Np/(N − ps). We prove that ground state solutions concentrate at a single point x̄ ∈ Ω and analyze the asymptotic behavior for sequences of solutions at higher energy levels. In the semi-linear case p = 2, we prove that for s...

We study the stability of the standing wave solutions of a Gross-Pitaevskii equation describing Bose-Einstein condensation of dipolar quantum gases and characterize their orbit. As an intermediate step, we consider the corresponding constrained minimization problem and establish existence, symmetry and uniqueness of the ground state solutions.

Structure of exact solutions modelling confinement is discussed for SU(3)-Yang-Mills equations and uniqueness of such confining solutions is proved in a certain sense. Relationship of the obtained results to QCD and the confinement mechanism is considered. Incidentally the Wilson confinement criterion for the found solutions is verified and also numerical estimates for strength of magnetic colo...