NON-EXISTENCE OF POSITIVE SOLUTIONS FOR A HIGHER ORDER FRACTIONAL EQUATION

Cui Xuewei; Yu Mei

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NON-EXISTENCE OF POSITIVE SOLUTIONS FOR A HIGHER ORDER FRACTIONAL EQUATION

机译：高阶分数阶方程的正解不存在

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摘要

In this paper, we consider a nonlinear equation involving fractional Laplacian of higher order on the whole space. We establish the equivalence between the pseudo-differential equation and an integral equation by applying the maximum principle and the Liouville theorem. For positive solutions to the equation, we obtained non-existence by applying the method of moving planes.

机译：在本文中，我们考虑了一个在整个空间上包含高阶分数拉普拉斯算子的非线性方程。通过应用最大值原理和Liouville定理，我们建立了伪微分方程和积分方程之间的等价关系。对于方程的正解，我们通过应用移动平面的方法获得了不存在的信息。

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来源
《Discrete and continuous dynamical systems》 |2019年第3期|1379-1387|共9页
作者
Cui Xuewei; Yu Mei;
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作者单位

Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China;

Northwestern Polytech Univ, Dept Appl Math, Xian 710072, Shaanxi, Peoples R China;

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正文语种 eng
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关键词
Fractional Laplacian of higher order; non-existence of solutions; maximum principle; Liouville theorem; the method of moving planes in integral form;

机译：高阶分数拉普拉斯算子;解的不存在;最大原理;Liouville定理;以整数形式移动平面的方法;

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2. Existence and non-existence of positive solutions of BVPs for fractional order elastic beam equations with a non-Caratheodory nonlinearity [J] . Yuji Liu Applied Mathematical Modelling . 2014,第2期

机译：具有非Caratheodory非线性分数阶弹性梁方程BVPs正解的存在性和不存在性
3. Non-existence of positive solutions of some elliptic equations in positive-type domains [J] . An TQ Applied mathematics letters . 2007,第6期

机译：正型域中某些椭圆型方程正解的不存在
4. Existence of Positive Solutions of Nonlinear Fractional Quadratic Differential Equations [C] . K. Hilal, Y. Allaoui, K. Guida International conference on intuitionistic fuzzy sets and its applications . 2019

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5. Positive solutions of higher order boundary value problems of nonlinear fractional differential equations. [D] . McCabe, Michael. 2014

机译：非线性分数阶微分方程的高阶边值问题的正解。
6. Multiple positive solutions to a coupled systems of nonlinear fractional differential equations [O] . Kamal Shah, Rahmat Ali Khan -1

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7. Non-existence and instantaneous extinction of solutions for singular nonlinear fractional diffusion equations [O] . Bonforte, Matteo, Segatti, Antonio, Vazquez, Juan Luis 2015

机译：奇异解的不存在与瞬时消亡非线性分数阶扩散方程

NON-EXISTENCE OF POSITIVE SOLUTIONS FOR A HIGHER ORDER FRACTIONAL EQUATION

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