Existence of solutions for some fourth-order boundary value problems with parameters

被引：28

作者：

Yang, Yang ^{[1
,2
]}

Zhang, Jihui ^{[1
]}

机构：

[1] Nanjing Normal Univ, Sch Math & Comp Sci, Inst Math, Nanjing, Peoples R China

[2] Jiangnan Univ, Sch Sci, Wuxi, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 69卷 / 04期

基金：

高等学校博士学科点专项科研基金;

关键词：

boundary value problem; homological nontrivial critical point; Morse theory; local linking;

D O I：

10.1016/j.na.2007.06.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, existence and multiplicity results for solutions are obtained for the fourth-order boundary value problem (BVP) u((4))(t) + eta u ''(t) - xi u(t) = lambda f(t, u(t)), 0 < t < 1, u(0) =u(1) =u ''(0) = u ''(1) =0, where f : [0, 1] x R -> R is continuous, xi, eta is an element of R and lambda is an element of R+ are parameters. By using the critical point theory and Morse theory, we obtain that if xi, eta satisfy xi/pi(4), eta/pi(2) < 1, then the above BVP has solutions where. is in some different intervals. (c) 206 Elsevier Ltd. All rights reserved.

引用

页码：1364 / 1375

页数：12

共 8 条

[1] Critical point theory for asymptotically quadratic functionals and applications to problems with resonance [J].

Bartsch, T ;

Li, SJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1997, 28 (03) :419-441

[2] Existence of solutions to nonlinear Hammerstein integral equations and applications [J].

Li, Fuyi ;

Li, Yuhua ;

Liang, Zhanping .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 323 (01) :209-227

[3] 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

[4] Remarks on multiple nontrivial solutions for quasi-linear resonant problems [J].

Liu, J ;

Su, JB .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2001, 258 (01) :209-222

[5] Existence and multiplicity of solutions for fourth-order boundary value problems with parameters [J].

Liu, Xi-Lan ;

Li, Wan-Tong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 327 (01) :362-375

[6]

Taylor A.E., 1980, INTRO FUNCTIONAL ANA

[7] Multiple nontrivial solutions for some fourth-order semilinear elliptic problems [J].

Zhang, JH ;

Li, SJ .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 60 (02) :221-230

[8]

刘嘉荃, 1989, Systems Science and Mathematical Science, V2, P32

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