Dirichlet BVP for the second order nonlinear ordinary differential equations at resonance
Landesman-Lazer’s type efficient sufficient conditions are established for the solvability of the Dirichlet problem , for where ;R) and f is the L([a,b]; R) Caratheodory function, in the case where the linear problem has nontrivial solutions. The results obtained in the paper are optimal in the sen...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2019-10-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/10202 |
| Summary: | Landesman-Lazer’s type efficient sufficient conditions are established for the solvability of the Dirichlet problem , for where ;R) and f is the L([a,b]; R) Caratheodory function, in the case where the linear problem has nontrivial solutions. The results obtained in the paper are optimal in the sense that if , i.e., when nonlinear equation turns to the linear equation, from our results follows the first part of Fredholm’s theorem.
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| ISSN: | 1392-6292 1648-3510 |