IJPAM: Volume 54, No. 1 (2009)

WEAKLY NONLINEAR BOUNDARY VALUE PROBLEMS
ON TIME SCALES

Rebecca I.B. Kalhorn$^1$, Jesús Rodríguez$^2$
$^{1,2}$Department of Mathematics
North Carolina State University
P.O. Box 8205, Raleigh, NC 27695-8205, USA
$^1$e-mail: [email protected]
$^2$e-mail: [email protected]


Abstract.We study weakly nonlinear boundary value problems on time scales. Our analysis is devoted to problems at resonance; that is, problems where the homogeneous linear boundary value problem has a nontrivial solution space. For these boundary value problems we establish conditions for the existence of solutions, and we discuss the dependence of solutions on parameters.

Received: June 7, 2009

AMS Subject Classification: 39B99, 39A10

Key Words and Phrases: boundary value problems, time scales, Lyapunov-Schmidt, resonance

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 54
Issue: 1