Multiple solutions for a class of fractional equations

被引：0

作者：

Pei, Ruichang ^{[1
]}

Zhang, Jihui ^{[2
]}

Ma, Caochuan ^{[1
]}

机构：

[1] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China

[2] Nanjing Normal Univ, Inst Math, Sch Math & Comp Sci, Nanjing 210097, Jiangsu, Peoples R China

来源：

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS | 2015年 / 93期

关键词：

fractional Laplacian; multiple solutions; asymptotically linear; mountain pass theorem; Morse theory;

D O I：

10.14232/ejqtde.2015.1.93

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study a class of fractional Laplace equations with asymptotically linear right-hand side. The existence results of three nontrivial solutions under the resonance and non-resonance conditions are established by using the minimax method and Morse theory.

引用

页数：12

共 18 条

[1] Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7
[2] On some critical problems for the fractional Laplacian operator
Barrios, B.
Colorado, E.
de Pablo, A.
Sanchez, U.
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (11) : 6133 - 6162
[3] Critical point theory for asymptotically quadratic functionals and applications to problems with resonance
Bartsch, T
Li, SJ
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (03) : 419 - 441
[4] Cabre X., 2009, ADV MATH, V42, P2052
[5] Cerami G., 1980, ANN MAT PUR APPL, V124, P161, DOI [10.1007/BF01795391, DOI 10.1007/BF01795391]
[6] Chang K.C., 1994, Topological Methods in Nonlinear Analysis, V3, P179, DOI [10.12775/TMNA.1994.008, DOI 10.12775/TMNA.1994.008]
[7] Chang Kung-ching, 1993, PROGR NONLINEAR DIFF, V6
[8] Asymptotically linear problems driven by fractional Laplacian operators
Fiscella, Alessio
Servadei, Raffaella
Valdinoci, Enrico
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2015, 38 (16) : 3551 - 3563
[9] Iannizzotto A., ADV CALC VAR
[10] Liu JQ, 2002, NONLINEAR ANAL-THEOR, V49, P779

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