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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2022
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet |
| Tárgyszavak: | |
| doi: | 10.14232/ejqtde.2022.1.11 |
| Online Access: | http://acta.bibl.u-szeged.hu/75826 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 27 |
| ISSN: | 1417-3875 |