Liouville Type Results For Polyharmonic Inequalities with Nonlocal Terms

Bei Wang *

School of Mathematics and Statistics, Southwest University, Chongqing 400715, People's Republic of China.

*Author to whom correspondence should be addressed.


In this note, we study the polyharmonic inequalities system
(-\Delta)^m u_i \geq \sum_{j=1}^n e_{i j}\left(\Psi_{i j}(|x|) * u_j^{p_{i j}}\right) u_i^{q_{i j}} \quad \text { in }{ }^N, \quad i=1,2, \cdots, n,
where \(N \geq 1\) and \(m \geq 1\) are integers, \(p_{i j} \geq 1, q_{i j}>0\). \(\Delta^m\) denotes the m-polyharmonic operator. The operator \(*\) denotes the convolution and \(\Psi_{i j}\) is a function that has certain properties. \(\left(e_{i j}\right)\) is the adjacency matrix. By poly-superharmonic propery of u and some estimates, we get a Liouville type result of (0.1), which generalize the recent results on these inequalities.

Keywords: Polyharmonic inequalities, nonlocal terms, liouville type results

How to Cite

Wang, B. (2023). Liouville Type Results For Polyharmonic Inequalities with Nonlocal Terms. Asian Journal of Mathematics and Computer Research, 30(2), 9–16.


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