Sunra Mosconi

The Brezis–Nirenberg problem for the fractional p-Laplacian

We obtain nontrivial solutions to the Brezis–Nirenberg problem for the fractional p-Laplacian operator, extending some results in the literature for the fractional Laplacian. The quasilinear case presents two serious new difficulties. First an explicit formula for a minimizer in the fractional Sobolev inequality is not available when

Heteroclinic Connections for the Swift-Hohenberg Equation with Multi-wells Potentials

p \ne 2

p

p≠2. We get around this difficulty by working with certain asymptotic estimates for minimizers recently obtained in (Brasco et al., Cal. Var. Partial Differ Equations 55:23, 2016). The second difficulty is the lack of a direct sum decomposition suitable for applying the classical linking theorem. We use an abstract linking theorem based on the cohomological index proved in (Yang and Perera, Ann. Sci. Norm. Super. Pisa Cl. Sci. doi:10.2422/2036-2145.201406_004, 2016) to overcome this difficulty.

-Laplacian

Abstract The existence of multiple solutions to a Dirichlet problem involving the ( p , q )

Optimal decay of extremals for the fractional Sobolev inequality

{(p,q)}

Hs versus C0-weighted minimizers

-Laplacian is investigated via variational methods, truncation-comparison techniques, and Morse theory. The involved reaction term is resonant at infinity with respect to the first eigenvalue of - Δ p

The abstract Lewy–Stampacchia inequality and applications

{-\Delta_{p}}

The Abresch-Gromoll inequality in a non-smooth setting

in W 0 1 , p ⁢ ( Ω )