具有变符号权函数的临界分数阶方程的多重性结果

IF 0.7 Q3 MATHEMATICS, APPLIED

Differential Equations & Applications Pub Date : 2021-01-01 DOI:10.7153/DEA-2021-13-09

Yang Pu, Jia‐Feng Liao

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引用次数: 0

摘要

．本文考虑一个与时间无关的分数阶方程，其中Ω是光滑有界域，s∈(0,1)，N bbb20 s 0 < q < 1，系数函数f和g可以改变符号。首先用Nehari方法得到了在系数函数联合作用下基态解的存在性。然后利用山口定理，在一些较强的条件下求出正解的多重性，其中一个正解是基态解。

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Multiplicity results for critical fractional equations with sign-changing weight functions

. In this paper, we consider a time-independent fractional equation: where Ω is a smooth bounded domain, s ∈ ( 0 , 1 ) , N > 2 s 0 < q < 1, the coef ﬁ cient functions f and g may change sign. We ﬁ rst obtain the existence of ground state solution by the Nehari method under the combined effect of coef ﬁ cient functions. Then we ﬁ nd the multiplicity of positive solutions by Mountain pass theorem under some stronger conditions, and one of them is a ground state solution.

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Differential Equations & Applications MATHEMATICS, APPLIED-

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