6 papers
On the emergence of dead cores in elliptic systems with sublinear competitive interactions
Hugo Tavares, Gianmaria Verzini, Junwei Yu
In this paper, we study semilinear elliptic systems with sublinear coupling terms, showing that, under competition-type interactions, solutions typically have dead cores, i.e., the…
Selection of the angular speed of rotating waves in segregated reaction-diffusion systems with asymmetric competition
Giuseppe Spadaro, Gianmaria Verzini, Alessandro Zilio
We investigate the existence of segregated rotating waves, arising in the singular limit of competition-diffusion systems of the type \[ \partial_t u_i -\partial_{xx} u_i = f(u_i)-…
Shape optimization of a small favorable region in a periodically fragmented environment
Gianmaria Verzini
We consider a shape optimization problem for the persistence threshold of a biological species dispersing in a periodically fragmented environment, the unknown shape corresponding…
Miminization of the first eigenvalue of the Dirichlet Laplacian with a small volume obstacle
Benedetta Noris, Giovanni Siclari, Gianmaria Verzini
We consider the well-known shape optimization problem with spectral cost: minimizing the first eigenvalue of the Dirichlet Laplacian among all subdomains having prescribed vol…
Energy local minimizers for the nonlinear Schrödinger equation on product spaces
Dario Pierotti, Gianmaria Verzini, Junwei Yu
We investigate the existence of local minimizers with prescribed -norm for the energy functional associated to the mass-supercritical nonlinear Schrödinger equation on the pr…
Normalized solutions for the nonlinear Schrödinger equation with potential: the purely Sobolev critical case
Gianmaria Verzini, Junwei Yu
We study the existence and multiplicity of positive solutions in , , with prescribed -norm, for the (stationary) nonlinear Schrödinger equation with…