IJPAM: Volume 63, No. 3 (2010)

MULTIPOINT BOUNDARY VALUE PROBLEMS FOR
DISCRETE NONLINEAR SYSTEMS AT RESONANCE

David H. Pollack$^1$, Padraic W. Taylor$^2$
$^{1,2}$Department of Mathematics and Statistics
Youngstown State University
1, University Plaza, Youngstown, Ohio, 44555, USA
$^1$email: [email protected]
$^2$email: [email protected]


Abstract.In this paper we provide sufficient conditions for the existence of solutions to multipoint boundary value problems for discrete nonlinear systems at resonance. We gain insight into the relationship between the nonlinearity and the solution space of the associated linear problem with the Lyapunov-Schmidt technique. Using degree theory we obtain results for systems, thereby extending previous work that used techniques applicable only to scalar equations.

Received: June 16, 2010

AMS Subject Classification: 39A10, 39A12

Key Words and Phrases: boundary value problems, degree theory, Lyapunov-Schmidt, multipoint, projection

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 63
Issue: 3