A non-existence result for higher-order Hardy-Hénon inequality on punctured balls
Từ khóa:
Hardy–Hénon polyharmonic equation, non–negative and classical solution, existence and non–existence, weak and strong super–polyharmonic properties
Tóm tắt
Let and be two positive integers such that . Let and be real such that and . In this note, we are mainly concerned with non-negative and classical solutions of the high-order harmonic inequality
on the punctured ball . Using the method of test functions, the Hölder's inequality, and integral estimates, we will prove that this inequality has no positive solution satisfying some sufficient conditions. It should be mentioned that our result, see Theorem 1.1 in the next section, in the high-order setting is analogous to that of Laptev for the case .
điểm /
đánh giá
Phát hành ngày
2024-08-30
Chuyên mục
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