一类四阶椭圆型问题及相关不等式的整体解

IF 3.2 1区数学 Q1 MATHEMATICS

Advances in Nonlinear Analysis Pub Date : 2022-01-01 DOI:10.1515/anona-2021-0217

L. D’Ambrosio, E. Mitidieri

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引用次数: 3

摘要

摘要我们研究了Δ2u+f（u）=0型双线性双调和方程的分布解在…上ℝN、｛\Delta^2｝u+f（u）=0\quad on \；｛\mathbb R｝^N｝，其中f是满足f（t）t≥c|t|q+1的连续函数，对于所有t∈ℝ 其中c>0和q>1。利用一种主要基于谨慎选择合适的加权检验函数的新方法和Hardy-Rellich不等式的新版本，我们证明了几个独立于维数N和解的符号的Liouville定理。

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Entire solutions of certain fourth order elliptic problems and related inequalities

Abstract We study distributional solutions of semilinear biharmonic equations of the type Δ2u+f(u)=0 onℝN, {\Delta ^2}u + f(u) = 0\quad on\;{{\mathbb R} ^N}, where f is a continuous function satisfying f (t)t ≥ c |t|q+1 for all t ∈ ℝ with c > 0 and q > 1. By using a new approach mainly based on careful choice of suitable weighted test functions and a new version of Hardy- Rellich inequalities, we prove several Liouville theorems independently of the dimension N and on the sign of the solutions.

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来源期刊

Advances in Nonlinear Analysis MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

6.00

自引率

9.50%

发文量

审稿时长

30 weeks

期刊介绍： Advances in Nonlinear Analysis (ANONA) aims to publish selected research contributions devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. The Journal focuses on papers that address significant problems in pure and applied nonlinear analysis. ANONA seeks to present the most significant advances in this field to a wide readership, including researchers and graduate students in mathematics, physics, and engineering.