Bifurcation interval for positive solutions to discrete second-order boundary value problems

Abstract

Let be an integer with , , . We give a global description of the branches of positive solutions of the nonlinear eigenvalue problem

which are not necessarily linearizable. Our approaches are based on topological degree and global bifurcation techniques.

Keywords:

• multiplicity
• difference equations
• positive solutions
• global bifurcation techniques
• eigenvalues

2000 Mathematics Subject Classification::

• 39A10
• 34G20

Acknowledgements

R. Ma was supported by the NSFC (No. 11061030), the NSF of Gansu Province (No. 3ZS051-A25-016), NWNU-KJCXGC-03-17, the Spring-sun program (No. Z2004-1-62033), SRFDP (No. 20060736001) and the SRF for ROCS, SEM (2006[311]).