6 papers
Asymptotic behavior of solutions for the nonlinear Hartree equation involving the fractional Laplacian
Natalino Borgia, Silvia Cingolani, Minbo Yang +1
In this paper, we investigate the nonlocal problem \begin{equation*}\left\lbrace \begin{aligned} &A_{s} u=(|x|^{-(n-2s)}\ast u^{2_{s}^{\sharp}-1-ε})u^{2_{s}^{\sharp}-2-ε} \quad\q…
Variational and Geometric Analysis for Quasilinear Elliptic Equations and Systems
Natalino Borgia
In this thesis we focus on quasilinear elliptic systems driven by various nonlinear operators, such as the p-Laplacian, and nonlinear sources that are allowed to exhibit both subcr…
On the de Thélin eigenvalue problem and Landesman-Lazer conditions for quasilinear systems
David Arcoya, Natalino Borgia, Silvia Cingolani
In this paper we prove that the smallest eigenvalue of the eigenvalue problem for a quasilinear elliptic systems introduced by de Thélin in \cite{DT}, is not only simple (i…
Uniform -boundedness for solutions of anisotropic quasilinear systems
Natalino Borgia, Silvia Cingolani, Giuseppina Vannella
In this paper we obtain uniformly locally -estimate of solutions to non-autonomous quasilinear system involving operators in divergence form and a family of nonlinearit…
On the equivalence between an Onofri-type inequality by Del Pino-Dolbeault and the sharp logarithmic Moser-Trudinger inequality
Natalino Borgia, Silvia Cingolani, Gabriele Mancini
In this paper we consider the -dimensional Euclidean Onofri inequality proved by del Pino and Dolbeault for smooth compactly supported functions in , . W…
New analytical and geometrical aspects on Trudinger-Moser type inequality in 2D
Natalino Borgia, Silvia Cingolani, Gabriele Mancini
The present survey is devoted to results on Trudinger-Moser inequalities in two dimension. We give a brief overview of the history of these celebrated inequalities and, starting fr…