Radial symmetry of positive solutions for a tempered fractional p-Laplacian system

Abstract

In this paper, we consider the following Schrödinger system involving the tempered fractional p-Laplacian

$$\begin{aligned} {\left\{ \begin{array}{ll} \begin{aligned} & (-\varDelta -\lambda )^s_p u(x)+au^{p-1}(x)=f(u(x),v(x)),\\ & (-\varDelta -\lambda )^t_p v(x)+bv^{p-1}(x)=g(u(x),v(x)), \end{aligned} \end{array}\right. } \end{aligned}$$

where \(n \ge 2\), \(a, b>0\), \(2<p<\infty \), \(0<s, t<1\) and \(\lambda \) is a sufficiently small positive constant. To effectively utilize the direct method of moving planes, we first establish the narrow region principle and the decay at infinity. Then we prove the radial symmetry and monotonicity of positive solutions for the system in the unit ball and the whole space. Our results are an extension of some content in Ma and Zhang (Appl Math J Chin Univ 37: 52–72, 2022).