IJPAM: Volume 54, No. 1 (2009)
WEAKLY NONLINEAR BOUNDARY VALUE PROBLEMS
ON TIME SCALES
ON TIME SCALES
Rebecca I.B. Kalhorn
, Jesús Rodríguez
Department of Mathematics
North Carolina State University
P.O. Box 8205, Raleigh, NC 27695-8205, USA
e-mail: riburton@ncsu.edu
e-mail: rodrigu@ncsu.edu
, Jesús Rodríguez
Department of Mathematics
North Carolina State University
P.O. Box 8205, Raleigh, NC 27695-8205, USA
e-mail: riburton@ncsu.edu
e-mail: rodrigu@ncsu.edu
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