Boundary Value Problems for a Super-Sublinear Asymmetric Oscillator: The Exact Number of Solutions. (28th February 2013)

• Record Type: Journal Article
• Authors: Gritsans, Armands; Sadyrbaev, Felix
• Other Names: Ricci Paolo Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2013(2013)
• Publication Date: 2013-02-28
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2013/705984
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : Properties of asymmetric oscillator described by the equation x ′′ = − λ ( x + ) p + μ ( x − ) q (i), where p ≥ 1 and 0 < q ≤ 1, are studied. A set of ( λ, μ ) such that the problem (i), x ( 0 ) = 0 = x ( 1 ) (ii), and | x ′ ( 0 ) | = α (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.