5 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…