Sixth Mississippi State Conference on Differential Equations and
Computational Simulations.
Electronic Journal of Differential Equations,
Conference 15 (2007), pp. 399-415. 

Title: Existence, multiplicity, and bifurcation in systems of
       ordinary differential equations

Author: James R. Ward Jr. (Univ. of Alabama, Birmingham, AL, USA)
 
Abstract: 
 We prove new non-resonance conditions for boundary value problems for two
 dimensional systems of ordinary differential equations. We apply these results
 to the existence of solutions to nonlinear problems. We then study global
 bifurcation for such systems of ordinary differential equations Rotation
 numbers are associated with solutions and are shown to be invariant along
 bifurcating continua. This invariance is then used to analyze the global
 structure of the bifurcating continua, and to demonstrate the existence of
 multiple solutions to some boundary value problems.

Published February 28, 2007.
Math Subject Classifications: 34B15, 47J10, 47J15.
Key Words: Global bifurcation; rotation number;
    Leray-Schauder degree; nonlinear boundary value problems.