Positive solutions to a semipositone superlinear elastic beam equation

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...

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Bibliographic Details
Published inAIMS mathematics Vol. 6; no. 5; pp. 4227 - 4237
Main Authors Lu, Haixia, Sun, Li
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2021
Subjects
elastic beam equations
fixed point
nontrivial solutions and positive solutions
topological degree
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2021250