Resonant Problems by Quasilinearization

The Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem ha...

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Main Author: Nadezhda Sveikate
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:International Journal of Differential Equations
Online Access:http://dx.doi.org/10.1155/2014/564914
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author Nadezhda Sveikate
author_facet Nadezhda Sveikate
author_sort Nadezhda Sveikate
collection DOAJ
description The Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem has a solution. We say then that the original problem allows for quasilinearization. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples.
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series International Journal of Differential Equations
spelling doaj-art-d8384d1781a34c26aba9e918abd8315f2025-08-20T03:23:51ZengWileyInternational Journal of Differential Equations1687-96431687-96512014-01-01201410.1155/2014/564914564914Resonant Problems by QuasilinearizationNadezhda Sveikate0Faculty of Natural Sciences and Mathematics, Daugavpils University, Parādes Street 1, Daugavpils 5401, LatviaThe Dirichlet resonant boundary value problems are considered. If the respective nonlinear equation can be reduced to a quasilinear one with a nonresonant linear part and both equations are equivalent in some domain Ω and if solutions of the quasilinear problem are in Ω, then the original problem has a solution. We say then that the original problem allows for quasilinearization. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions. We give conditions for Emden-Fowler type resonant boundary value problem solvability and consider examples.http://dx.doi.org/10.1155/2014/564914
spellingShingle Nadezhda Sveikate
Resonant Problems by Quasilinearization
International Journal of Differential Equations
title Resonant Problems by Quasilinearization
title_full Resonant Problems by Quasilinearization
title_fullStr Resonant Problems by Quasilinearization
title_full_unstemmed Resonant Problems by Quasilinearization
title_short Resonant Problems by Quasilinearization
title_sort resonant problems by quasilinearization
url http://dx.doi.org/10.1155/2014/564914
work_keys_str_mv AT nadezhdasveikate resonantproblemsbyquasilinearization