On multi-bump solutions for the Choquard-Kirchhoff equations in $ \mathbb{R}^{N} $.

Liang, Shuaishuai; Sun, Mingzhe; Shi, Shaoyun; Liang, Sihua

In this paper, we investigate the following Choquard-Kirchhoff equations in $ \mathbb{R}^{N} $:$ \begin{eqnarray*} \left\{\begin{array}{l} - K_b(u) (\lambda V(x) 1)|u|^{p-2}u = \left(\frac{1}{|x|^{\mu}} *F(u)\right)f(u)\ \ \mbox{in } \,\mathbb{R}^{N},\\ u \in W^{1,p}(\mathbb{R}^{N}), \end{array}\right. \end{eqnarray*} $where $ K_b(u) = \biggl(1 b \int_{\mathbb{R}^{N}}|\nabla u|^{p} dx\biggl)\Delta_pu $, $ \Delta_p $ is the $ p $-Laplacian operator, $ 0 0 $ large enough, the above equation has at least $ 2^{k}-1 $ multi-bump solutions.

CONTINUOUS functions; EQUATIONS; LAPLACIAN operator; POTENTIAL well

Discrete & Continuous Dynamical Systems - Series S, 2023, Vol 16, Issue 11, p1

1937-1632

Academic Journal

10.3934/dcdss.2023012