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Existence and multiplicity of positive solutions of certain nonlocal scalar field equations

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  • Mousomi Bhakta
  • Souptik Chakraborty
  • Debdip Ganguly

Abstract

We study existence and multiplicity of positive solutions of the following class of nonlocal scalar field equations: P${\mathcal {P}}$ (−Δ)su+u=a(x)|u|p−1u+f(x)inRNu∈Hs(RN),$$\begin{equation} \hspace*{5pc} {\left\lbrace \begin{aligned} (-\Delta )^s u + u &= a(x) |u|^{p-1}u+f(x)\;\;\text{in}\;\mathbb {R}^{N}\\ u &\in H^{s}{\big(\mathbb {R}^{N}\big)}, \end{aligned} \right.} \end{equation}$$where s∈(0,1)$s \in (0,1)$, N>2s$N>2s$, 1

Suggested Citation

  • Mousomi Bhakta & Souptik Chakraborty & Debdip Ganguly, 2023. "Existence and multiplicity of positive solutions of certain nonlocal scalar field equations," Mathematische Nachrichten, Wiley Blackwell, vol. 296(9), pages 3816-3855, September.
    • Handle: RePEc:bla:mathna:v:296:y:2023:i:9:p:3816-3855
    DOI: 10.1002/mana.202000473
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