四阶弹性梁方程特征值问题正解的存在性

陆海霞

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

数学季刊 >

2017 , Vol. 32 >Issue 1: 7 - 15

DOI: https://doi.org/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

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School of Arts and Science,Suqian College

LU Hai-xia(1976-), female, native of Jianhu, Jiangsu, an associate professor of Suqian College,M.S.D., engages in nonlinear functional analysis.

收稿日期: 2016-05-13

网络出版日期: 2020-10-26

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)；

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

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School of Arts and Science,Suqian College

LU Hai-xia(1976-), female, native of Jianhu, Jiangsu, an associate professor of Suqian College,M.S.D., engages in nonlinear functional analysis.

Received date: 2016-05-13

Online published: 2020-10-26

Supported by

Supported by the National Natural Science Foundation of China(11501260)； Supported by the National Natural Science Foundation of Suqian City(Z201444)；

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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

本文引用格式

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

Abstract

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

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