Nonlocal problems at critical growth in contractible domains

Article type: Research Article

Authors: Mosconi, Sunra^a | Shioji, Naoki^b | Squassina, Marco^{a; *}

Affiliations: [a] Dipartimento di Informatica, Università degli Studi di Verona, Verona, Italy. E-mails: [email protected], [email protected] | [b] Department of Mathematics, Faculty of Engineering, Yokohama National University, Yokohama, Japan. E-mail: [email protected]

Correspondence: [*] Corresponding author: Marco Squassina, Dipartimento di Informatica, Università degli Studi di Verona, Cá Vignal 2, Strada Le Grazie 15, 37134 Verona, Italy. E-mail: [email protected].

Abstract: We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.

Keywords: fractional equation, critical embedding, contractible domains, existence

DOI: 10.3233/ASY-151324

Journal: Asymptotic Analysis, vol. 95, no. 1-2, pp. 79-100, 2015