Multipe solutions for a nonlocal fractional $(p,q)$-Schr\"odinger-Kirchhoff system

  • Elhoussine Azroul Laboratory of Mathematical Analysis and Applications, Department of Mathematics
  • Abdelmoujib Benkirane Laboratory of Mathematical Analysis and Applications, Department of Mathematics,
  • Athmane Boumazourh Laboratory of Mathematical Analysis and Applications, Department of Mathematics
  • Mohammed Srati Sidi Mohammed Ben Abdellah University

Abstract

In this paper, we study the existence of multiple weak solutions for a Schr\"odinger-Kirchhoff type elliptic system involving nonlocal $(p,q)-$integro-differential operators :
$$
\hspace*{0.5cm} \left\{
\begin{array}{clclc}

M_1\left( I_{K,p}(u)\right) \left(\mathcal{L}^K_p u+V(x)|u|^{p-2}u\right) = \lambda F_u(x,u,v)+\mu G_u(x,u,v) & \text{ in }& \R^N, \\\\
M_2\left( I_{K,q}(v)\right) \left(\mathcal{L}^K_q v+V(x)|v|^{q-2}v\right) = \lambda F_v(x,u,v)+\mu G_v(x,u,v) & \text{ in }& \R^N.
\end{array}
\right.
$$
The technical approach is mainly based on three critical points theorem.

Published
2020-11-23