4 papers
A Brezis-Nirenberg type result for mixed local and nonlocal operators
Stefano Biagi, Serena Dipierro, Enrico Valdinoci +1
We study a critical problem for an operator of mixed order obtained by the superposition of a Laplacian with a fractional Laplacian. In particular, we investigate the corresponding…
Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
Stefano Biagi, Fabio Punzo, Eugenio Vecchi
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator , with a power-like source ter…
On the existence of a second positive solution to mixed local-nonlocal concave-convex critical problems
Stefano Biagi, Eugenio Vecchi
We prove the existence of a second positive weak solution for mixed local-nonlocal critical semilinear elliptic problems with a sublinear perturbation in the spirit of [Ambrosetti,…
Multiplicity of positive solutions for mixed local-nonlocal singular critical problems
Stefano Biagi, Eugenio Vecchi
We prove the existence of at least two positive weak solutions for mixed local-nonlocal singular and critical semilinear elliptic problems in the spirit of [Haitao, 2003], extendin…