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Subject: nonlocal equations ×

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    A critical Kirchhoff type problem involving a non-local operator
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.
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    On stable solutions of boundary reaction-diffusion equations and applications to nonlocal problems with Neumann data
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 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.