95 citations · 149 across the 12 of their papers we have counts for
13 papers
New multiplicity results for critical -Laplacian problems
Carlo Mercuri, Kanishka Perera
We prove new multiplicity results for the Brezis-Nirenberg problem for the -Laplacian. Our proofs are based on a new abstract critical point theorem involving the ${\mathbb Z}_2…
Groundstates and infinitely many high energy solutions to a class of nonlinear Schrödinger-Poisson systems
Tomas Dutko, Carlo Mercuri, Teresa Megan Tyler
We study a nonlinear Schrödinger-Poisson system which reduces to the nonlinear and nonlocal equation \[- Δu+ u + λ^2 \left(\frac{1}{ω|x|^{N-2}}\star ρu^2\right) ρ(x) u = |u|^{q-1}…
Quantitative symmetry breaking of groundstates for a class of weighted Emden-Fowler equations
Carlo Mercuri, Ederson Moreira dos Santos
We consider a class of weighted Emden-Fowler equations \begin{equation} \tag{} \label{eqab} \left\{\begin{array}{ll} -Δu=V_α (x) \, u^p & \text{in} \,\,B,\\ u>0 & \te…
Groundstate asymptotics for a class of singularly perturbed -Laplacian problems in
Wedad Albalawi, Carlo Mercuri, Vitaly Moroz
We study the asymptotic behavior of positive groundstate solutions to the quasilinear elliptic equation \begin{equation} -Δ_{p} u + \varepsilon u^{p-1} - u^{q-1} +u^{\mathit{l}-1}…
On a class of nonlinear Schrödinger-Poisson systems involving a nonradial charge density
Carlo Mercuri, Teresa Megan Tyler
In the spirit of the classical work of P. H. Rabinowitz on nonlinear Schrödinger equations, we prove existence of mountain-pass solutions and least energy solutions to the nonlinea…
A Liouville theorem for the -Laplacian and related questions
Alberto Farina, Carlo Mercuri, Michel Willem
We prove several classification results for -Laplacian problems on bounded and unbounded domains, and deal with qualitative properties of sign-changing solutions to -Laplacia…
Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb-Sobolev spaces
Jacopo Bellazzini, Marco Ghimenti, Carlo Mercuri +2
We prove scaling invariant Gagliardo-Nirenberg type inequalities of the form $$\|φ\|_{L^p(\mathbb{R}^d)}\le C\|φ\|_{\dot H^{s}(\mathbb{R}^d)}^β \left(\iint_{\mathbb{R}^d \times \ma…
A regularity result for the p-laplacian near uniform ellipticity
Carlo Mercuri, Giuseppe Riey, Berardino Sciunzi
We consider weak solutions to a class of Dirichlet boundary value problems invloving the -Laplace operator, and prove that the second weak derivatives are in with as…
Groundstates and radial solutions to nonlinear Schrödinger-Poisson-Slater equations at the critical frequency
Carlo Mercuri, Vitaly Moroz, Jean Van Schaftingen
We study the nonlocal Schrödinger-Poisson-Slater type equation where , ,…
On Coron's problem for the p-Laplacian
Carlo Mercuri, Berardino Sciunzi, Marco Squassina
We prove that the critical problem for the -Laplacian operator admits a nontrivial solution in annular shaped domains with sufficiently small inner hole. This extends Coron's pr…
On the pure critical exponent problem for the -Laplacian
Carlo Mercuri, Filomena Pacella
In this paper we prove existence and multiplicity of positive and sign-changing solutions to the pure critical exponent problem for the -Laplacian operator with Dirichlet bounda…
Global compactness for a class of quasi-linear elliptic problems
Carlo Mercuri, Marco Squassina
We prove a global compactness result for Palais-Smale sequences associated with a class of quasi-linear elliptic equations on exterior domains.
Concentration on circles for nonlinear Schrödinger-Poisson systems with unbounded potentials vanishing at infinity
Denis Bonheure, Jonathan Di Cosmo, Carlo Mercuri
The present paper is devoted to weighted Nonlinear Schrödinger- Poisson systems with potentials possibly unbounded and vanishing at infinity. Using a purely variational approach, w…