2013, Fiscella, Alessio, Valdinoci, Enrico

We show the existence of non-negative solutions for a Kirchhoff type problem driven by a non-local integrodifferential operator.

2015, Dipierro, Serena, Soave, Nicola, Valdinoci, Enrico

We study reaction-diffusion equations in cylinders with possibly nonlinear diffusion and possibly nonlinear Neumann boundary conditions. We provide a geometric Poincare-type inequality and classification results for stable solutions, and we apply them to the study of an associated nonlocal problem. We also establish a counterexample in the corresponding framework for the fractional Laplacian.