Global Behavior of the Components for the Second Order <inline-formula> <graphic file="1687-2770-2008-254593-i1.gif"/></inline-formula>-Point Boundary Value Problems

• Main Authors: An Yulian, Ma Ruyun
• Format: Article
• Language: English
• Published: SpringerOpen 2008-01-01
• Series: Boundary Value Problems
• Online Access: http://www.boundaryvalueproblems.com/content/2008/254593
• ISSN: 1687-2762; 1687-2770

<p>Abstract</p> <p>We consider the nonlinear eigenvalue problems <inline-formula> <graphic file="1687-2770-2008-254593-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-254593-i3.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-254593-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-254593-i5.gif"/></inline-formula>, where <inline-formula> <graphic file="1687-2770-2008-254593-i6.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-254593-i7.gif"/></inline-formula>, and <inline-formula> <graphic file="1687-2770-2008-254593-i8.gif"/></inline-formula> for <inline-formula> <graphic file="1687-2770-2008-254593-i9.gif"/></inline-formula>, with <inline-formula> <graphic file="1687-2770-2008-254593-i10.gif"/></inline-formula>; <inline-formula> <graphic file="1687-2770-2008-254593-i11.gif"/></inline-formula>; <inline-formula> <graphic file="1687-2770-2008-254593-i12.gif"/></inline-formula>. There exist two constants <inline-formula> <graphic file="1687-2770-2008-254593-i13.gif"/></inline-formula> such that <inline-formula> <graphic file="1687-2770-2008-254593-i14.gif"/></inline-formula> and <inline-formula> <graphic file="1687-2770-2008-254593-i15.gif"/></inline-formula>, <inline-formula> <graphic file="1687-2770-2008-254593-i16.gif"/></inline-formula>. Using the global bifurcation techniques, we study the global behavior of the components of nodal solutions of the above problems.</p>