arXiv subjects
Publications and source records attributed to Marcelo Furtado.
In this paper we establish a new class of weighted Hardy-Sobolev type inequalities under mild monotonicity assumptions on the weight function. As a consequence, we derive the corresponding weighted Sobolev and trace-type inequalities. These results play an important role in the analysis of elliptic problems with Neumann or Robin boundary conditions in unbounded domains.
In this paper we are concerned with nonlinear Schrödinger equations with random potentials. Our class includes continuum and discrete potentials. Conditions on the potential $V_ω$ are found for existence of solutions almost sure $ω$. We study probabilistic properties like central limit theorem and law of larger numbers for the obtained solutions by independent ensembles. We also give estimates on the expected value for the $L^{\infty}$-norm of the solution showing how it depends on the size of the potential.