Some problems of ionospheric nonlinearities

Truncation of Nonlinearities in Some Supercritical Elliptic Problems

We consider truncations of nonlinearities of semilinear elliptic problems by H 1 , not necessarily bounded, sub and super solutions. We prove that their associated energy functionals are of class C 1 and satisfy the Palais{Smale condition. We apply this result to prove existence of innnitely many solutions of a supercritical elliptic problem involving concave and convex nonlinearities. Troncatu...

Dirichlet Problems with Asymmetric Nonlinearities

Combined effects of concave-convex nonlinearities and indefinite potential in some elliptic problems

We consider a nonlinear Dirichlet problem driven by the p-Laplacian and a reaction which exhibits the combined effects of concave (that is, sublinear) terms and of convex (that is, superlinear) terms. The concave term is indefinite and the convex term need not satisfy the usual in such cases Ambrosetti–Rabinowitz condition. We prove a bifurcation-type result describing the set of positive solut...

Ionospheric F-region storms: unsolved problems

Befitting the venue of this meeting, we first investigate the polar ionosphere. The most pressing problem here is that no reliable description of this region is available, not even for undisturbed conditions. To improve on this situation we have investigated the properties of some of the more prominent anomalies observed in this region, including the heating effect below the magnetospheric cusp...

Some Remarks on Biharmonic Elliptic Problems with Positive, Increasing and Convex Nonlinearities

We study the existence of positive solutions for a fourth order semilinear elliptic equation under Navier boundary conditions with positive, increasing and convex source term. Both bounded and unbounded solutions are considered. When compared with second order equations, several differences and difficulties arise. In order to overcome these difficulties new ideas are needed. But still, in some ...