Multiple solutions of some nonlinear fourth-order beam equations

Guodong Han; Zongben Xu

doi:10.1016/j.na.2007.04.007

Multiple solutions of some nonlinear fourth-order beam equations

Guodong Han
, Zongben Xu

数学与统计学院

Xi'an Jiaotong University

科研成果: 期刊稿件 › 文章 › 同行评审

91 引用（Scopus）

摘要

Several new existence theorems on three solutions and infinitely many solutions for the following fourth-order beam equation are obtained: u⁽⁴⁾ = f (t, u (t)), t ∈ [0, 1] ; u (0) = u (1) = u^″ (0) = u^″ (1) = 0, where f ∈ C¹ ([0, 1] × R¹, R¹). The Morse theory is employed to discuss this problem.

源语言	英语
页（从-至）	3646-3656
页数	11
期刊	Nonlinear Analysis, Theory, Methods and Applications
卷	68
期	12
DOI	https://doi.org/10.1016/j.na.2007.04.007
出版状态	已出版 - 15 6月 2008

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10.1016/j.na.2007.04.007

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abstract = "Several new existence theorems on three solutions and infinitely many solutions for the following fourth-order beam equation are obtained: u(4) = f (t, u (t)), t ∈ [0, 1] ; u (0) = u (1) = u″ (0) = u″ (1) = 0, where f ∈ C1 ([0, 1] {\texttimes} R1, R1). The Morse theory is employed to discuss this problem.",

keywords = "Boundary value problems, Critical group, Critical points, Morse inequality",

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N2 - Several new existence theorems on three solutions and infinitely many solutions for the following fourth-order beam equation are obtained: u(4) = f (t, u (t)), t ∈ [0, 1] ; u (0) = u (1) = u″ (0) = u″ (1) = 0, where f ∈ C1 ([0, 1] × R1, R1). The Morse theory is employed to discuss this problem.

AB - Several new existence theorems on three solutions and infinitely many solutions for the following fourth-order beam equation are obtained: u(4) = f (t, u (t)), t ∈ [0, 1] ; u (0) = u (1) = u″ (0) = u″ (1) = 0, where f ∈ C1 ([0, 1] × R1, R1). The Morse theory is employed to discuss this problem.

KW - Boundary value problems

KW - Critical group

KW - Critical points

KW - Morse inequality

UR - https://www.scopus.com/pages/publications/42949092555

U2 - 10.1016/j.na.2007.04.007

DO - 10.1016/j.na.2007.04.007

M3 - 文章

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 12

ER -

Multiple solutions of some nonlinear fourth-order beam equations

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