James R. Ward Jr.
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.
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| James R. Ward Jr. Department of Mathematics University of Alabama at Birmingham Birmingham, AL 35294, USA email: jrw87@math.uab.edu |
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