Positive solutions to three classes of non-local fourth-order problems with derivative-dependent nonlinearities

In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under the boundary conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound on the third-order derivative term, a...

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Bibliographic Details
Published inElectronic journal of qualitative theory of differential equations Vol. 2022; no. 11; pp. 1 - 27
Main Author Zhang, Guowei
Format Journal Article
LanguageEnglish
Published University of Szeged 01.01.2022
Subjects
cone
fixed point index
gronwall inequality
positive solution
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ISSN1417-3875
1417-3875
DOI10.14232/ejqtde.2022.1.11

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Summary:In the article, we investigate three classes of fourth-order boundary value problems with dependence on all derivatives in nonlinearities under the boundary conditions involving Stieltjes integrals. A Gronwall-type inequality is employed to get an a priori bound on the third-order derivative term, and the theory of fixed-point index is used on suitable open sets to obtain the existence of positive solutions. The nonlinearities have quadratic growth in the third-order derivative term. Previous results in the literature are not applicable in our case, as shown by our examples.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2022.1.11