An existence result for a class of quasilinear elliptic eigenvalue problems in unbounded domains

We consider a nonlinear eigenvalue problem under Robin boundary conditions in a domain with (possibly noncompact) smooth boundary. The problem involves a weighted p–Laplacian operator and subcritical nonlinearities satisfying Ambrosetti–Rabinowitz type conditions. Using Morse theory and a cohomological local splitting as in Degiovanni et al. (Commun Contemp Math 12:475–486, 2010), we prove the existence of a nontrivial weak solution for all (real) values of the eigenvalue parameter. Our result is new even in the semilinear case p = 2 and complements some recent results obtained in Autuori et al. (Adv Anal Equ 18:1–48, 2013).     

Existence and multiplicity results for hemivariational inequalities with two parameters

A multiplicity result of Ricceri, based on a minimax inequality, is applied to locally Lipschitz functionals and the existence of one or two non-trivial solutions for a class of two-parameter hemivariational inequalities is proved. An application is given to elliptic problems with discontinuous nonlinearities on unbounded domains.     

On 1-Blocking Sets in PG(n,q), n ≥ 3

In this article we study minimal1-blocking sets in finite projective spaces _PG(n,q),n 3. We prove that in PG(n,q ²),q = p ^h , p prime, p > 3,h 1, the second smallest minimal 1-blockingsets are the second smallest minimal blocking sets, w.r.t.lines, in a plane of PG(n,q ²). We also study minimal1-blocking sets in PG(n,q ³), n 3, q = p ^h, p prime, p > 3,q 5, and prove that the minimal 1-blockingsets of cardinality at most q 3 + q ² + q + ¹ are eithera minimal blocking set in a plane or a subgeometry PG(3,q).     

The external demagnetizing factor and the static characteristic loop

In this paper a proposal is put forward for the calculation of the shearing factor N_S linked to the well known, demagnetization coefficient N_D, from the data of a sheared saturation loop, obtained by a non-toroidal, open circuit hysteresis measurement. Following that, the paper illustrates the way to recover the real static loop data from an open circuit, measured data. The proposal is based on the hyperbolic model. The proposed method was illustrated on the tests carried out on two closed and open toroidal samples, mimicking the demagnetization effect of the open circuit VSM measurement, made of NO Fe–Si electrical steel sheets. These test results, presented here, agree very well with the calculated results, based on the hyperbolic modeling.