Existence of multiple positive solutions for a truncated Kirchhoff-type system involving weight functions and concave-convex nonlinearities

被引：1

作者：

Lou, Qingjun ^{[1
]}

Qin, Yupeng ^{[2
]}

机构：

[1] Univ Jinan, Sch Math Sci, Jinan, Peoples R China

[2] Henan Inst Technol, Sch Sci, Xinxiang, Henan, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2020年 / 2020卷 / 01期

关键词：

Kirchhoff system; Multiple positive solutions; Nehari manifold; NEHARI MANIFOLD; EQUATION; BEHAVIOR;

D O I：

10.1186/s13662-020-02556-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the combined effect of concave-convex nonlinearities on the number of solutions for an indefinite truncated Kirchhoff-type system involving the weight functions. When alpha+beta< 4+, since the concave-convex nonlinearities do not satisfy the mountain pass geometry, it is difficult to obtain a bounded Palais-Smale sequence by the usual mountain pass theorem. To overcome the problem, we properly introduce a method of Nehari manifold and then establish the existence of multiple positive solutions when the pair of the parameters is under a certain range.

引用

页数：13

共 24 条

[1] Existence results for a class of Kirchhoff type systems with Caffarelli-Kohn-Nirenberg exponents [J].

Afrouzi, G. A. ;

Zahmatkesh, H. ;

Shakeri, S. .

ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2016, 24 (01) :83-94

[2] Nonlocal fourth-order Kirchhoff systems with variable growth: low and high energy solutions [J].

Afrouzi, Ghasem A. ;

Mirzapour, M. ;

Radulescu, Vicentiu D. .

COLLECTANEA MATHEMATICA, 2016, 67 (02) :207-223

[3] Non-standard finite difference and Chebyshev collocation methods for solving fractional diffusion equation [J].

Agarwal, P. ;

El-Sayed, A. A. .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2018, 500 :40-49

[4]

Agarwal P., 2017, ADV REAL COMPLEX ANA

[5] A semilinear elliptic system involving nonlinear boundary condition and sign-changing weight function [J].

Brown, K. J. ;

Wu, Tsung-Fang .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 337 (02) :1326-1336

[6] The Nehari manifold for a semilinear elliptic equation with a sign-changing weight function [J].

Brown, KJ ;

Zhang, YP .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2003, 193 (02) :481-499

[7] The Nehari manifold for indefinite semilinear elliptic systems involving critical exponent [J].

Chen, Ching-yu ;

Wu, Tsung-fang .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (22) :10817-10828

[8] The Nehari manifold for a Kirchhoff type problem involving sign-changing weight functions [J].

Chen, Ching-yu ;

Kuo, Yueh-cheng ;

Wu, Tsung-fang .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2011, 250 (04) :1876-1908

[9] VARIATIONAL PRINCIPLE [J].

EKELAND, I .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1974, 47 (02) :324-353

[10] Multiplicity of solutions for a class of Kirchhoff type problems [J].

He, Xiao-ming ;

Zou, Wen-ming .

ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES, 2010, 26 (03) :387-394

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