Symmetry and monotonicity of positive solutions to Schrödinger systems with fractional p-Laplacians

• Published in: Applied Mathematics-A Journal of Chinese Universities 2022-03, Vol.37 (1), p.52-72
• Main Authors: Ma, Ling-wei, Zhang, Zhen-qiu
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Mathematics; Mathematics and Statistics; Symmetry
• ISSN: 1005-1031; 1993-0445
• DOI: 10.1007/s11766-022-4263-6

In this paper, we first establish narrow region principle and decay at infinity theorems to extend the direct method of moving planes for general fractional p -Laplacian systems. By virtue of this method, we investigate the qualitative properties of positive solutions for the following Schrödinger system with fractional p -Laplacian { ( − Δ ) p s u + a u p − 1 = f ( u v ) ( − Δ ) p t v + b v p − 1 = g ( u v ) where 0 < s, t < 1 and 2 < p < ∞. We obtain the radial symmetry in the unit ball or the whole space ℝ N ( N ≥ 2), the monotonicity in the parabolic domain and the nonexistence on the half space for positive solutions to the above system under some suitable conditions on f and g , respectively.