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International Journal of Mathematics and Mathematical Sciences
Volume 2013, Article ID 705984, 9 pages
http://dx.doi.org/10.1155/2013/705984
Research Article

Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions

Daugavpils University, Department of Mathematics, Parades Street 1, 5400 Daugavpils, Latvia

Received 30 March 2012; Accepted 5 November 2012

Academic Editor: Paolo Ricci

Copyright © 2013 Armands Gritsans and Felix Sadyrbaev. 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

Properties of asymmetric oscillator described by the equation (i), where and , are studied. A set of such that the problem (i), (ii), and (iii) have a nontrivial solution, is called α-spectrum. We give full description of α-spectra in terms of solution sets and solution surfaces. The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i), and (ii) is given.