Positive solutions to a semipositone superlinear elastic beam equation

Haixia Lu; Li Sun; Haixia Lu; Li Sun

doi:10.3934/math.2021250

AIMS Mathematics

2021, Volume 6, Issue 5: 4227-4237. doi: 10.3934/math.2021250

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Positive solutions to a semipositone superlinear elastic beam equation

Haixia Lu ^{1,2
,
,},
Li Sun ¹

1.
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, 221116, P. R. China
2.
School of arts and science, Suqian College, Suqian 223800, P. R. China

Received: 11 October 2020 Accepted: 04 January 2021 Published: 07 February 2021
MSC : 34K10, 37C25

A semipositone fourth-order two-point boundary value problem is considered. In mechanics, the problem describes the deflection of an elastic beam rigidly fastened on the left and simply supported on the right. Under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, the existence of nontrivial solutions and positive solutions to this boundary value problem is obtained. The main results are obtained by using the topological method and the fixed point theory of superlinear operators.
- topological degree,
- fixed point,
- nontrivial solutions and positive solutions,
- elastic beam equations
Citation: Haixia Lu, Li Sun. Positive solutions to a semipositone superlinear elastic beam equation[J]. AIMS Mathematics, 2021, 6(5): 4227-4237. doi: 10.3934/math.2021250

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Abstract

A semipositone fourth-order two-point boundary value problem is considered. In mechanics, the problem describes the deflection of an elastic beam rigidly fastened on the left and simply supported on the right. Under some conditions concerning the first eigenvalue corresponding to the relevant linear operator, the existence of nontrivial solutions and positive solutions to this boundary value problem is obtained. The main results are obtained by using the topological method and the fixed point theory of superlinear operators.

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