Keywords: Dirichlet boundary value problem p-Laplacian Topological degree theory Critical point theory Weak solution a b s t r a c t In this work, by virtue of topological degree theory and critical point theory, we are mainly concerned with the existence of weak solutions for a Dirichlet boundary value problem with the p-Laplacian operator.

It is shown that hadronic matter formed at high temperatures, according to the prescription of the statistical bootstrap principle, develops a critical point at nonzero baryon chemical potential, associated with the end point of a first-order, quark-hadron phase-transition line. The overall self-consistency of strong interactions suggests that this singularity must coincide with the QCD critica...

It is shown that hadronic matter formed at high temperatures, according to the prescription of the statistical bootstrap principle, develops a critical point at nonzero baryon chemical potential, associated with the end point of a first-order, quark-hadron phase-transition line. The overall self-consistency of strong interactions suggests that this singularity must coincide with the QCD critica...

It is shown that hadronic matter formed at high temperatures, according to the prescription of the statistical bootstrap principle, develops a critical point at nonzero baryon chemical potential, associated with the end point of a first-order, quark-hadron phase-transition line. The overall self-consistency of strong interactions suggests that this singularity must coincide with the QCD critica...

The asymptotic solution for the Painleve-2 equation with small parameter is considered. The solution has algebraic behavior before point t∗ and fast oscillating behavior after the point t∗. In the transition layer the behavior of the asymptotic solution is more complicated. The leading term of the asymptotics satisfies the Painleve-1 equation and some elliptic equation with constant coefficient...

It is shown that hadronic matter formed at high temperatures, according to the prescription of the statistical bootstrap principle, develops a critical point at nonzero baryon chemical potential. The location of the critical point in the phase diagram, however, depends on the detailed knowledge of the partition function of the deconfined phase, near the critical line. In a simplified version of...

We review the recent proposal that the most fascinating brain properties are related to the fact that it always stays close to a second order phase transition. In such conditions, the collective of neuronal groups can reliably generate robust and flexible behavior, because it is known that at the critical point there is the largest abundance of metastable states to choose from. Here we review t...

We study electric, thermal, and thermoelectric conductivities in the vicinity of a z = 2 superconductor-diffusive metal transition in two dimensions, both in the high and low frequency limits. We find violation of the Wiedemann-Franz law and a dc thermoelectric conductivity α that does not vanish at low temperatures, in contrast to Fermi liquids. We introduce a Langevin equation formalism to st...

A special asymptotic solution of the Painlevé-2 equation with small parameter is studied. This solution has a critical point t∗ corresponding to a bifurcation phenomenon. When t < t∗ the constructed solution varies slowly and when t > t∗ the solution oscillates very fast. We investigate the transitional layer in detail and obtain a smooth asymptotic solution, using a sequence of scaling and mat...