Multiple Positive Solutions for Fractional Schrödinger–Poisson System with Doubly Critical Exponents

• Autores: Wei Jiang, Jia-Feng Liao
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 1, 2023
• Idioma: inglés
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• Resumen

  • In this article, we study the following fractional Schrödinger–Poisson system (−)su + V(x)u − φ|u| 2∗ s −3u = |u| 2∗ s −2u + λ f (x), x ∈ R3, (−)sφ = |u| 2∗ s −1, x ∈ R3, where s ∈ (0, 1), 2∗ s = 6 3−2s , λ > 0 is a real parameter, f and V satisfy some suitable hypothesis. Via applying the variational methods and mountain pass theorem, we prove that there exists λ∗ > 0 such that the system has at least two positive solutions for any λ ∈ (0, λ∗) which supplements and generalizes the previous results in the literature.