Existence and multiplicity of solutions for a class of fractional elliptic systems

• Autores: Manassés de Souza
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 71, Fasc. 1, 2020, págs. 103-122
• Idioma: inglés
• DOI: 10.1007/s13348-019-00253-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • In this paper we are concerned with the existence and multiplicity of solutions of the following nonlocal system involving the fractional Laplacian \begin{aligned} (-\Delta )^\sigma u_i + a_i(x) u_i = f_i(x,u_1,\ldots ,u_m)\quad \text{ for }\;\; x \in \mathbb {R}^n \quad \text{ and }\;\; i=1,\ldots ,m, \end{aligned} where \sigma \in (0,1), n \ge 1, (-\Delta )^\sigma denotes the fractional Laplacian of order \sigma, a_i(x) are continuous and unbounded potentials which may change sign, and the nonlinearities f_i(x,u_1,\ldots ,u_m) are continuous functions which may be unbounded in x. We treat both the superquadratic situation and the nonquadratic situation at infinity on the nonlinearities f_i(x,u_1,\ldots ,u_m).