Consider the quasilinear Schrödinger equation$ -\Delta u+V(x)u-\frac12 \Delta(u^2)u = h(u)+\mu l(u),\ \ u\in H^1({\mathbb{R}}^N), $where \begin{document}$ V(x) $\end{document} is a radial potential allowed to be singular at x 0 $\end{document}, h an odd nonlinearity of Berestycki-Lions type, \mu\in{\mathbb{R}} small parameter and l general function. While most works in literature are restricted...

During their post – main-sequence evolution, massive star models harbor a convection zone on top of their hydrogen burning shell. This physical property helps, under suitable circumstances, to destabilize low-degree nonradial modes that might explain the cyclic light variability of α Cygni variables. The results of first exploratory computations demonstrate that modes with periods ranging from ...

Soft gamma repeaters are identified as highly magnetized (B≈ 10 14 Gauss) neutron stars. Magnetic stresses induce tectonic activity, and field annihilation in faults is the ultimate energy source for the observed γ-ray emission. As a consequence of the crustal cracking, the stored elastic energy is converted into high frequency (kHz) shear waves, that excite nonradial oscillation modes damped b...

The lack of a general maximum principle for biharmonic equations suggests to study under which boundary conditions the positivity preserving property holds. We show that this property holds in general domains for suitable linear combinations of Dirichlet and Navier boundary conditions. The spectrum of this operator exhibits some unexpected features: radial data may generate nonradial solutions....