Existence and Multiplicity of Solutions for a Fractional Schrödinger–Poisson System with Subcritical or Critical Growth

• Autores: Guangze Gu, Changyang Mu, Zhipeng Yang
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 2, 2023
• Idioma: inglés
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• Resumen

  • In this paper, we study the existence of positive ground state solutions and infinitely many geometrically distinct solutions for the following fractional Schrödinger– Poisson system (−)su + V(x)u + φu = f (x, u), in R3, (−)sφ = u2, in R3, where s ∈ ( 3 4 , 1) is a fixed constant, f is continuous, superlinear at infinity with subcritical or critical growth and V and f are asymptotically periodic in x. Applying the method of Nehari manifold and Lusternik–Schnirelmann category theory, three existence results are given.