四阶弹性梁方程特征值问题正解的存在性

doi:10.13371/j.cnki.chin.q.j.m.2017.01.002

数学季刊 ›› 2017, Vol. 32 ›› Issue (1): 7-15.doi: 10.13371/j.cnki.chin.q.j.m.2017.01.002

四阶弹性梁方程特征值问题正解的存在性

School of Arts and Science,Suqian College

收稿日期:2016-05-13 出版日期:2017-03-30 发布日期:2020-10-26
作者简介:LU Hai-xia(1976-), female, native of Jianhu, Jiangsu, an associate professor of Suqian College,M.S.D., engages in nonlinear functional analysis.
基金资助:
Supported by the National Natural Science Foundation of China(11501260)； Supported by the National Natural Science Foundation of Suqian City(Z201444)；

Existence of Positive Solutions for Eigenvalue Problems of Fourth-order Elastic Beam Equations

School of Arts and Science,Suqian College

Received:2016-05-13 Online:2017-03-30 Published:2020-10-26
About author:LU Hai-xia(1976-), female, native of Jianhu, Jiangsu, an associate professor of Suqian College,M.S.D., engages in nonlinear functional analysis.
Supported by:
Supported by the National Natural Science Foundation of China(11501260)； Supported by the National Natural Science Foundation of Suqian City(Z201444)；

摘要/Abstract

摘要： In this paper, we investigate the positive solutions of fourth-order elastic beam equations with both end-points simply supported. By using the approximation theorem of completely continuous operators and the global bifurcation techniques, we obtain the existence of positive solutions of elastic beam equations under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, when the nonlinear term is non-singular or singular, and allowed to change sign.

关键词: elastic beam equations, singular, positive solutions, global bifurcation

Abstract: In this paper, we investigate the positive solutions of fourth-order elastic beam equations with both end-points simply supported. By using the approximation theorem of completely continuous operators and the global bifurcation techniques, we obtain the existence of positive solutions of elastic beam equations under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, when the nonlinear term is non-singular or singular, and allowed to change sign.

Key words: elastic beam equations, singular, positive solutions, global bifurcation

中图分类号:

O175.8

陆海霞. 四阶弹性梁方程特征值问题正解的存在性[J]. 数学季刊, 2017, 32(1): 7-15.

LU Hai-xia. Existence of Positive Solutions for Eigenvalue Problems of Fourth-order Elastic Beam Equations[J]. Chinese Quarterly Journal of Mathematics, 2017, 32(1): 7-15.

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四阶弹性梁方程特征值问题正解的存在性

Existence of Positive Solutions for Eigenvalue Problems of Fourth-order Elastic Beam Equations

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