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
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• Resumen

  • In this paper we are concerned with the existence and multiplicity of solutions of the following nonlocal system involving the fractional Laplacian (−Δ)???+??(?)??=??(?,?1,…,??) for ?∈ℝ? and ?=1,…,?, where ?∈(0,1), ?≥1, (−Δ)? denotes the fractional Laplacian of order ?, ??(?) are continuous and unbounded potentials which may change sign, and the nonlinearities ??(?,?1,…,??) are continuous functions which may be unbounded in x. We treat both the superquadratic situation and the nonquadratic situation at infinity on the nonlinearities ??(?,?1,…,??).