We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...

This paper is devoted to the existence of positive solutions of a Dirichlet problem with critical exponent and a singular potential. Under various assumption on the domain O; which include some kinds of unbounded domains, we prove the existence of ground states and of symmetric solutions. r 2002 Elsevier Science (USA). All rights reserved.

Let Ω ⊂ RN be a smooth bounded domain such that 0 ∈ Ω , N ≥ 5, 0 ≤ s < 2, 2∗(s) = 2(N−s) N−2 . We prove the existence of nontrivial solutions for the singular critical problem − u − μ u |x |2 = |u| 2∗(s)−2 |x |s u + λu with Dirichlet boundary condition on Ω for all λ > 0 and 0 ≤ μ < ( N−2 2 )2 − ( N+2 N )2. © 2005 Elsevier Ltd. All rights reserved. MSC: 35J60; 35B33

This paper is concerned with the existence of nontrivial solutions for a class of degenerate quasilinear elliptic systems involving critical Hardy-Sobolev type exponents. The lack of compactness is overcame by using the Brezis-Nirenberg approach, and the multiplicity result is obtained by combining a version of the Ekeland’s variational principle due to Mizoguchi with the Ambrosetti-Rabinowitz ...

the coherent anomaly method and a cluster mean-field approach combined with finite-sizescaling extrapolation were used to determine the critical temperature and the critical exponents of as =1 ising chain with a long-range interaction in the form of 1/ r1+σ . the results of criticaltemperature are in good agreement with the recent results of the finite-range scaling method and aremore accurate ...