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Abstract and Applied Analysis
Volume 2015 (2015), Article ID 302185, 6 pages
http://dx.doi.org/10.1155/2015/302185
Research Article

Multiple Positive Solutions for the Dirichlet Boundary Value Problems by Phase Plane Analysis

1Daugavpils University, 13 Vienības Street, Daugavpils LV-5401, Latvia
2Institute of Mathematics and Computer Science of University of Latvia, Raina Bulvaris 29, Riga LV-1469, Latvia

Received 1 July 2015; Accepted 28 September 2015

Academic Editor: Jaume Giné

Copyright © 2015 A. Kirichuka and F. 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

We consider boundary value problems for scalar differential equation , , , where is a seventh-degree polynomial and is a parameter. We use the phase plane method combined with evaluations of time-map functions and make conclusions on the number of positive solutions. Bifurcation diagrams are constructed and examples are considered illustrating the bifurcation processes.