Least energy solutions for nonlinear fractional Choquard–Kirchhoff equations in $ {\mathbb{R}} ^N $
Year: 2025
Type: article
Abstract: In this paper, we investigate the following fractional Choquard–Kirchhoff type equation:$ \begin{align*} \left(a+b\iint_{{\mathbb{R}} ^{2N}} \frac{|u(x)-u(y)|^{2}}{|x-y|^{N+2s}}\, dxdy\right)(-\Delta)^{s}u+ u = \left(I_\alpha * F(u)\right) F'(u) \quad\mbox{ in } {\mathbb{R}} ^{N}, \end{align*} $where $ N\geq 2 $, $ a, b>0 $ are constants, $ (-\Delta)^{s} $ is the fractional Laplacian operator of order $ s\in(0, 1) $, $ I_\alpha $ denotes the Riesz potential of order $ \alpha \in((N-4s)_{+}, N) $, $ F\in C^{1}({\mathbb{R}} ) $ is a general nonlinearity of Berestycki–Lions type. Applying suitable variational methods, we prove the existence of a least energy solution. Moreover, assuming that $ F $ is even and monotone in $ (0, \infty) $, we show that the constructed solution has constant sign, is radially symmetric and decreasing.
DOI: 10.3934/dcds.2025076
Institution: Marche Polytechnic University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4410898171