一类包含分数阶p- laplace的kirchhoff型方程解的多重性和渐近性。

IF 1.6 3区数学 Q1 Mathematics

Journal of Inequalities and Applications Pub Date : 2018-01-01 Epub Date: 2018-05-10 DOI:10.1186/s13660-018-1708-9

Liejun Shen

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引用次数: 1

摘要

本文研究的是下列分数阶p-拉普拉斯方程，涉及Kirchhoff型临界Sobolev指数:[公式:见文]，其中[公式:见文]，[公式:见文]和[公式:见文]是常数，[公式:见文]是具有[公式:见文]和[公式:见文]的分数阶p-拉普拉斯算子。对于合适的[公式:见文]，上述方程对任意[公式:见文]至少具有两个非平凡解。并且，我们将[公式:见文]和[公式:见文]作为参数，得到给定问题解的收敛性质分别为[公式:见文]和[公式:见文]。

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Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional p-Laplacian.

The present study is concerned with the following fractional p-Laplacian equation involving a critical Sobolev exponent of Kirchhoff type: [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text] are constants, and [Formula: see text] is the fractional p-Laplacian operator with [Formula: see text] and [Formula: see text]. For suitable [Formula: see text], the above equation possesses at least two nontrivial solutions by variational method for any [Formula: see text]. Moreover, we regard [Formula: see text] and [Formula: see text] as parameters to obtain convergent properties of solutions for the given problem as [Formula: see text] and [Formula: see text], respectively.

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来源期刊

Journal of Inequalities and Applications MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

3.30

自引率

6.20%

发文量

136

审稿时长

3 months

期刊介绍： The aim of this journal is to provide a multi-disciplinary forum of discussion in mathematics and its applications in which the essentiality of inequalities is highlighted. This Journal accepts high quality articles containing original research results and survey articles of exceptional merit. Subject matters should be strongly related to inequalities, such as, but not restricted to, the following: inequalities in analysis, inequalities in approximation theory, inequalities in combinatorics, inequalities in economics, inequalities in geometry, inequalities in mechanics, inequalities in optimization, inequalities in stochastic analysis and applications.