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International Journal of Differential Equations
Volume 2014 (2014), Article ID 564914, 8 pages
http://dx.doi.org/10.1155/2014/564914
Research Article

Resonant Problems by Quasilinearization

Faculty of Natural Sciences and Mathematics, Daugavpils University, Parādes Street 1, Daugavpils 5401, Latvia

Received 29 January 2014; Accepted 6 March 2014; Published 22 April 2014

Academic Editor: Ioannis G. Stratis

Copyright © 2014 Nadezhda Sveikate. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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 and if solutions of the quasilinear problem are in , 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.