FRACTIONAL EQUATIONS WITH INDEFINITE NONLINEARITIES

Chen Wenxiong; Li Congming; Zhu Juiyi

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FRACTIONAL EQUATIONS WITH INDEFINITE NONLINEARITIES

机译：带有不确定非线性的分数阶方程

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摘要

In this paper, we consider a fractional equation with indefinite nonlinearities(-Delta)(alpha/2)u = a(x(1))f(u)for 0 alpha 2, where a and f are nondecreasing functions. We prove that there is no positive bounded solution. In particular, in the case a(x(1)) = x(1) and f(u) = u(P), this remarkably improves the result in [15] by extending the range of alpha from [1, 2) to (0, 2), due to the introduction of new ideas, which may be applied to solve many other similar problems.

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来源
《Discrete and continuous dynamical systems》 |2019年第3期|1257-1268|共12页
作者
Chen Wenxiong; Li Congming; Zhu Juiyi;
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作者单位

Yeshiva Univ, Dept Math Sci, New York, NY 10033 USA;

Shanghai Jiao Tong Univ, Sch Math, Shanghai, Peoples R China;

Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA;

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正文语种 eng
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关键词
The fractional Laplacian; indefinite nonlinearities; method of moving planes; monotonicity; non-existence of positive solutions;

机译：分数拉普拉斯算子;不确定非线性;运动平面法;单调性;不存在正解;

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FRACTIONAL EQUATIONS WITH INDEFINITE NONLINEARITIES

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