Ground State Solutions for Kirchhoff-type Problems with Critical Nonlinearity

被引：9

作者：

Ye, Yiwei ^{[1
]}

机构：

[1] Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2020年 / 24卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Kirchhoff-type equation; ground state solutions; variational methods; POSITIVE SOLUTIONS; ELLIPTIC-EQUATIONS; MULTIPLICITY; EXISTENCE; R-3;

D O I：

10.11650/tjm/190402

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the Kirchhoff-type equation with critical exponent -(a + b integral(R3) vertical bar Vu vertical bar(2) dx) Delta u + V(x)u = a(x)f (u) + u(5) in R-3 where a, b > 0 are constants, V is an element of C(R-3, R), lim(vertical bar x vertical bar) (-> infinity) V(x) = V-infinity > 0 and V(x) <= V-infinity + C(1)e(-b vertical bar x vertical bar) for some C-1 > 0 and vertical bar x vertical bar large enough. Via variational methods, we prove the existence of ground state solution.

引用

页码：63 / 79

页数：17

共 27 条

[1] Nonlinear perturbations of a periodic Kirchhoff equation in RN [J].

Alves, Claudianor O. ;

Figueiredo, Giovany M. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2012, 75 (05) :2750-2759

[2]

Ambrosetti A., 1973, Journal of Functional Analysis, V14, P349, DOI 10.1016/0022-1236(73)90051-7

[3] Multiple positive solutions to a class of Kirchhoff equation on R3 with indefinite nonlinearity [J].

Chen, Jianqing .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2014, 96 :134-145

[4] Existence of a positive solution for a Kirchhoff problem type with critical growth via truncation argument [J].

Figueiredo, Giovany M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2013, 401 (02) :706-713

[5]

He Y, 2014, ADV NONLINEAR STUD, V14, P483

[6] ON FINDING SOLUTIONS OF A KIRCHHOFF TYPE PROBLEM [J].

Huang, Yisheng ;

Liu, Zeng ;

Wu, Yuanze .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2016, 144 (07) :3019-3033

[7]

Kirchhoff G., 1883, MECHANIK

[8] The existence of a positive solution to asymptotically linear scalar field equations [J].

Li, G ;

Zhou, HS .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2000, 130 :81-105

[9] Existence and multiplicity of solutions for the Kirchhoff equations with asymptotically linear nonlinearities [J].

Li, Lin ;

Sun, Ji-Jiang .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2015, 26 :391-399

[10]

Lions J. L., 1978, P INT S CONT MECH PA, V30, P284, DOI DOI 10.1016/S0304-0208(08)70870-3

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