Solutions of p(x)-Laplacian equations with

critical exponent and perturbations in RN.

The critical behavior of the sound attenuation coefficient in the neighborhood of the second-order phase transition points is characterized by the dynamical sound attenuation

critical exponent [rho].

There are a few works about the nonsingular magnetic problems with

critical exponents, such as [9,14,15] for Sobolev

critical exponent and [16] for Hardy

critical exponent.

fraction (1 wt%) of CNTs for PI nanocomposites at the

critical exponent t= 1.7.

In fact, in combinatorics and in statistical physics, most of the asymptotics of integer sequences are of the shape [b.sub.n] ~ C[n.sup.[alpha]] [A.sup.n], and the exponent [alpha] which appears there is a key quantity: its value is often the signature of some universal phenomena (in physics, it is called a

critical exponent).

Santra, "Uniqueness and profile of positive solutions of a

critical exponent problem with Hardy potential," Journal of Differential Equations, vol.

[4] J.G.Azvrero, I.P.Aloson, Multiplicity of solutions for elliptic problems with

critical exponent or with a nonsymmetric term, Trans.

Let [k.sub.c]: = min{k [member of] Z - {0}|[a.sub.k] [not equal to] 0}, then [alpha] = [k.sub.c]/N is called the

critical exponent (loosely speaking, [alpha] is the "first non zero exponent" appearing in the series, and if [z.sub.0] is not precised, it is by default the radius of convergence of f(z)).

where [phi] is the volume fraction of filler, [p.sub.c] is the percolation threshold of filler, [[rho].sub.f] is the resistivity of the filler, [r.sub.l] is the resistivity of the polymer or matrix, and p is the

critical exponent which represents the volume fraction of the phases.

Rocha, Four solutions of an inhomogeneous elliptic equation with

critical exponent and singular term, Nonlinear Anal.