A class of singular fourth-order boundary value problems with nonhomogeneous nonlinearity

被引：1

作者：

Yao, Qingliu ^{[1
]}

机构：

[1] Nanjing Univ Finance & Econ, Dept Appl Math, Nanjing 210003, Jiangsu, Peoples R China

来源：

ANNALES POLONICI MATHEMATICI | 2013年 / 109卷 / 03期

基金：

中国国家自然科学基金;

关键词：

singular differential equation; boundary value problem; positive solution; existence; ELASTIC BEAM EQUATION; POSITIVE SOLUTIONS; SUFFICIENT CONDITION; UNIQUENESS THEOREMS; SPACE SINGULARITIES; EXISTENCE; MULTIPLICITY; CONJUGATE; TIME; 4TH;

D O I：

10.4064/ap109-3-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.

引用

页码：311 / 325

页数：15

共 32 条

[1] EXISTENCE AND UNIQUENESS THEOREMS FOR 4TH-ORDER BOUNDARY-VALUE-PROBLEMS [J].

AFTABIZADEH, AR .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1986, 116 (02) :415-426

[2] Multiplicity results for singular conjugate, focal, and (n, p) problems [J].

Agarwal, RP ;

O'Regan, D .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 170 (01) :142-156

[3] On positive solutions of some nonlinear fourth-order beam equations [J].

Bai, ZB ;

Wang, HY .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 270 (02) :357-368

[4] Existence and uniqueness theorems for fourth-order singular boundary value problems [J].

Cui, Yujun ;

Zou, Yumei .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2009, 58 (07) :1449-1456

[5]

Curtain R., 1977, FUNCTIONAL ANAL MODE

[6] EXISTENCE FOR A 4TH-ORDER BOUNDARY-VALUE PROBLEM UNDER A 2-PARAMETER NONRESONANCE CONDITION [J].

DELPINO, MA ;

MANASEVICH, RF .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 112 (01) :81-86

[7] Singular nonlinear (k,n-k) conjugate boundary value problems [J].

Eloe, PW ;

Henderson, J .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1997, 133 (01) :136-151

[8] EXISTENCE AND UNIQUENESS RESULTS FOR THE BENDING OF AN ELASTIC BEAM EQUATION AT RESONANCE [J].

GUPTA, CP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1988, 135 (01) :208-225

[9] Nonresonant singular fourth-order boundary value problems [J].

Jiang, DQ ;

Liu, HZ ;

Xu, XJ .

APPLIED MATHEMATICS LETTERS, 2005, 18 (01) :69-75

[10] Existence and multiplicity of solutions of a kind of fourth-order boundary value problem [J].

Li, FY ;

Zhang, Q ;

Liang, ZP .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 62 (05) :803-816

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