一类分数阶椭圆方程非平凡解的多重性

IF 0.9 4区数学 Q2 MATHEMATICS Journal of Integral Equations and Applications Pub Date : 2021-10-01 DOI:10.1216/jie.2021.33.315

T. Kenzizi

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引用次数: 1

摘要

本文研究了分数阶拉普拉斯方程(−∆)u = a(x)|u(x)|q−2u(x) + λb(x)|u(x)|p−2u(x) In(−1,1)，u > In(−1,1)，u = 0 In R(−1,1)，其中s∈(0,1)，λ > 0。利用变分方法，证明了正解的存在性和多重性。

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Multiplicity of nontrivial solutions for a class of fractional elliptic equations

In this paper, we are concerned with the following fractional Laplacian equation (−∆)u = a(x)|u(x)|q−2u(x) + λb(x)|u(x)|p−2u(x) in (−1, 1), u > 0 in (−1, 1), u = 0 in R (−1, 1), where s ∈ (0, 1), λ > 0. Using variational methods, we show existence and multiplicity of positive solutions.

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来源期刊

Journal of Integral Equations and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Integral Equations and Applications is an international journal devoted to research in the general area of integral equations and their applications. The Journal of Integral Equations and Applications, founded in 1988, endeavors to publish significant research papers and substantial expository/survey papers in theory, numerical analysis, and applications of various areas of integral equations, and to influence and shape developments in this field. The Editors aim at maintaining a balanced coverage between theory and applications, between existence theory and constructive approximation, and between topological/operator-theoretic methods and classical methods in all types of integral equations. The journal is expected to be an excellent source of current information in this area for mathematicians, numerical analysts, engineers, physicists, biologists and other users of integral equations in the applied mathematical sciences.