Existence results of positive solutions of Kirchhoff type problems

被引：182

作者：

Cheng, Bitao ^{[1
,2
]}

Wu, Xian ^{[1
]}

机构：

[1] Yunnan Normal Univ, Dept Math, Kunming 650092, Yunnan, Peoples R China

[2] Qujing Normal Univ, Dept Math & Informat Sci, Qujing 655011, Yunnan, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 10期

基金：

中国国家自然科学基金;

关键词：

Critical point; Positive solution; Kirchhoff type problems; Sobolev inequality; NONTRIVIAL SOLUTIONS; EQUATION;

D O I：

10.1016/j.na.2009.03.065

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we use variational methods to prove two existence results of positive solutions of the following Kirchhoff type problems {-(a + b integral(Omega)vertical bar del u vertical bar(2)) Delta u = f(x, u), in Omega; u =0, on partial derivative Omega. One deals with the asymptotic behaviors of f near zero and infinity and the other deals with 4-superlinear of f at infinity. (C) 2009 Elsevier Ltd. All rights reserved.

引用

页码：4883 / 4892

页数：10

共 17 条

[1] Positive solutions for a quasilinear elliptic equation of Kirchhoff type [J].

Alves, CO ;

Corrêa, FJSA ;

Ma, TF .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2005, 49 (01) :85-93

[2] On the well-posedness of the Kirchhoff string [J].

Arosio, A ;

Panizzi, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1996, 348 (01) :305-330

[3]

Bernstein S., 1940, Bull. Acad. Sci. URSS. Sr. Math. (Izvestia Akad. Nauk SSSR), V4, P17

[4]

Cavalcanti MM., 2001, Adv. Differential Equations, V6, P701

[5]

Cerami G., 1978, Ren. Acad. Sci. Lett. Ist. Lomb, V112, P332

[6] Some remarks on non local elliptic and parabolic problems [J].

Chipot, M ;

Lovat, B .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 30 (07) :4619-4627

[7] NONTRIVIAL SOLUTIONS FOR PERTURBATIONS OF THE P-LAPLACIAN ON UNBOUNDED-DOMAINS [J].

COSTA, DG ;

MIYAGAKI, OH .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1995, 193 (03) :737-755

[8] GLOBAL SOLVABILITY FOR THE DEGENERATE KIRCHHOFF EQUATION WITH REAL ANALYTIC DATA [J].

DANCONA, P ;

SPAGNOLO, S .

INVENTIONES MATHEMATICAE, 1992, 108 (02) :247-262

[9]

Falk Martin, TOURISM MANAGE, V29, P1172, DOI [10.1016/j.tourman.2008.02.021, DOI 10.1016/J.TOURMAN.2008.02.021]

[10]

HE X, 2008, NONLINEAR ANAL, DOI DOI 10.1016/J.NA.2008.02.011

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