Qualitative properties and existence of sign changing solutions with compact support for an equation with a p-Laplace operator

We consider radial solutions of an elliptic equation involving the p-Laplace operator and prove by a shooting method the existence of compactly supported solutions with any prescribed number of nodes. The method is based on a change of variables in the phase plane corresponding to an asymptotic Hamiltonian system and provides qualitative properties of the solutions

BPS Skyrme neutron stars in generalized gravity

We study the coupling of nuclear matter described by the BPS Skyrme model to generalized gravity. Concretely, we consider the Starobinsky model which provides the leading-order correction to the Einstein-Hilbert action. Static solutions describing neutron stars are found both for the full field theory and for the mean-field approximation. We always consider the full Starobinsky model in the nonperturbative approach, using appropriately generalized shooting methods for the numerical neutron star calculations. Many of our results are similar to previous investigations of neutron stars for the Starobinsky model using other models of nuclear matter, but there are some surprizing discrepancies. The "Newtonian mass" relevant for the surface redshift, e.g., results larger than the ADM mass in our model, in contrast to other investigations. This difference is related to the particularly high stiffness of nuclear matter described by the BPS Skyrme model and offers an interesting possibility to distinguish different models of nuclear matter within generalized gravity.Comment: LaTex, 28 pages, 13 figures; v2: minor change

The effects of retardation on the topological plasmonic chain: plasmonic edge states beyond the quasistatic limit

We study a one-dimensional plasmonic system with non-trivial topology: a chain of metallic nanoparticles with alternating spacing, which is the plasmonic analogue to the Su-Schreiffer-Heeger model. We extend previous efforts by including long range hopping with retardation and radiative damping, which leads to a non-Hermitian Hamiltonian with frequency dependence. We calculate band structures numerically and show that topological features such as quantised Zak phase persist due to chiral symmetry. This predicts parameters leading to topologically protected edge modes, which allows for positioning of disorder-robust hotspots at topological interfaces, opening up novel nanophotonics applications

On Regions of Existence and Nonexistence of solutions for a System of pp-qq-Laplacians

We give a new region of existence of solutions to the superhomogeneous Dirichlet problem \quad \begin{array}{l} -\Delta_{p} u= v^\delta\quad v>0\quad {in}\quad B,\cr -\Delta_{q} v = u^{\mu}\quad u>0\quad {in}\quad B, \cr u=v=0 \quad {on}\quad \partial B, \end{array}\leqno{(S_R)} where $B$ is the ball of radius $R>0$ centered at the origin in \RR^N. Here $\delta, \mu >0$ and $\Delta_{m} u={\rm div}(|\nabla u|^{m-2}\nabla u)$ is the $m-$Laplacian operator for $m>1$.Comment: 17 pages, accepted in Asymptotic Analysi