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Global Behavior of the Components for the Second Order https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq1_HTML.gif -Point Boundary Value Problems

Boundary Value Problems20072008:254593

DOI: 10.1155/2008/254593

Received: 9 October 2007

Accepted: 16 December 2007

Published: 24 December 2007

Abstract

We consider the nonlinear eigenvalue problems https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq2_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq3_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq4_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq5_HTML.gif , where https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq6_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq7_HTML.gif , and https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq8_HTML.gif for https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq9_HTML.gif , with https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq10_HTML.gif ; https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq11_HTML.gif ; https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq12_HTML.gif . There exist two constants https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq13_HTML.gif such that https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq14_HTML.gif and https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq15_HTML.gif , https://static-content.springer.com/image/art%3A10.1155%2F2008%2F254593/MediaObjects/13661_2007_Article_796_IEq16_HTML.gif . Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.

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Authors’ Affiliations

(1)
Department of Mathematics, Northwest Normal University
(2)
Department of Mathematics, Lanzhou Jiaotong University

Copyright

© Y. An and R. Ma. 2008

This article is published under license to BioMed Central Ltd. 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.