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Variational methods for scaled functionals with applications to the Schrödinger-Poisson-Slater equation
Carlo Mercuri, Kanishka Perera
We develop novel variational methods for solving scaled equations that do not have the mountain pass geometry, classical linking geometry based on linear subspaces, or $\mathbb Z_2…
Positive solutions to nonlinear elliptic problems involving Sobolev exponent
Carlo Mercuri, Riccardo Molle
In this paper we consider nonlinear elliptic PDEs of the type $$-Δ_p u+a(x)|u|^{p-2}u=|u|^{p^*-2}u \qquad \mbox{ in }Ω,$$ where and is the critical Sobolev e…
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…
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…