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

Mousomi Bhakta, Souptik Chakraborty and Debdip Ganguly

Mathematische Nachrichten, 2023, vol. 296, issue 9, 3816-3855

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

Date: 2023
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