Symmetries in an overdetermined problem for the Green's function [PDF]
arXiv, 2009 We consider in the plane the problem of reconstructing a domain from the normal derivative of its Green's function with pole at a fixed point in the domain. By means of the theory of conformal mappings, we obtain existence, uniqueness, (non-spherical) symmetry results, and a formula relating the curvature of the boundary of the domain to the normal ...
arxiv
Outbreak of Klebsiella pneumoniae ST11 Resistant To Ceftazidime-Avibactam Producing KPC-31 and the Novel Variant KPC-115 during COVID-19 Pandemic in Argentina. [PDF]
Microbiol Spectr, 2022 Nicola F +9 more
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Solutions to nonlinear Schrödinger equations with singular electromagnetic potential and critical exponent [PDF]
arXiv, 2010 We investigate existence and qualitative behaviour of solutions to nonlinear Schr\"odinger equations with critical exponent and singular electromagnetic potentials. We are concerned with magnetic vector potentials which are homogeneous of degree -1, including the Aharonov-Bohm class.
arxiv
On Struwe-Jeanjean-Toland monotonicity trick [PDF]
arXiv, 2010 The abstract version of Struwe's monotonicity trick developed by Jeanjean and Jeanjean-Toland for functionals depending on a real parameter is improved, under suitable assumptions. Besides, all the machinery is extended to the case of continuous functionals on Banach spaces, in the framework of non-smooth critical point theory.
arxiv
Mountain pass solutions for quasi-linear equations via a monotonicity trick [PDF]
arXiv, 2011 We obtain the existence of mountain pass solutions for quasi-linear equations without the typical assumptions which guarantee the boundedness of an arbitrary Palais-Smale sequence. This is done through a recent version of the monotonicity trick proved by the second author. The main results are new also for the p-Laplacian operator.
arxiv
On the Gibbons' conjecture for equations involving the $p$-Laplacian [PDF]
arXiv, 2020 In this paper we prove the validity of Gibbons' conjecture for the quasilinear elliptic equation $ -\Delta_p u = f(u) $ on $\mathbb{R}^N.$ The result holds true for $(2N+2)/(N+2) < p < 2$ and for a very general class of nonlinearity $f$.
arxiv
On a bifurcation value related to quasi-linear Schrodinger equations [PDF]
arXiv, 2011 By virtue of numerical arguments we study a bifurcation phenomenon occurring for a class of minimization problems associated with the quasi-linear Schrodinger equation.
arxiv
Radial Symmetry of Large Solutions of Semilinear Elliptic Equations with Convection [PDF]
arXiv, 2012 We study radial symmetry of large solutions of the semi-linear elliptic problem \Delta u + \nabla h.\nabla u = f(|x|,u), and we provide sharp conditions under which the problem has a radial solution. The result is independent of the rate of growth of the solution at infinity.
arxiv
Symmetry of n-mode positive solutions for two-dimensional Hénon type systems [PDF]
arXiv, 2013 We provide a symmetry result for n-mode positive solutions of a general class of semi-linear elliptic systems under cooperative conditions on the nonlinearities. Moreover, we apply the result to a class of H\'enon systems and provide the existence of multiple n-mode positive solutions.
arxiv
Asymptotics of ground states for fractional Hénon systems [PDF]
arXiv, 2014 We investigate the asymptotic behavior of positive ground states for H\'enon type systems involving a fractional Laplacian on a bounded domain, when the powers of the nonlinearity approach the Sobolev critical exponent.
arxiv