Halflinear Dynamic Equations: A Survey
 Citation data:

Nonlinear Analysis and Applications
 Publication Year:
 2003
 Repository URL:
 http://scholarsmine.mst.edu/math_stat_facwork/209
 Author(s):
 Publisher(s):
 Tags:
 dynamic equations; time scales; halflinear equations; Sturmian theory; oscillation; Reid roundabout theorem; Picone Identity; dynamic equations; time scales; halflinear equations; Sturmian theory; oscillation; Reid roundabout theorem; Picone Identity; Mathematics; Statistics and Probability
article description
We survey halflinear dynamic equations on time scales. These contain the wellknown halflinear di erential and halflinear di erence equations as special cases, but also other kinds of halflinear equations. Special cases of halflinear equations are the wellstudied linear equations of second order. We discuss existence and uniqueness of solutions of corresponding initial value problems and, using a Picone identity, derive a Reid roundabout theorem that gives conditions equivalent to disconjugacy of halflinear dynamic equations, among them solvability of an associated Riccati equation and positive de niteness of an associated functional. We also develop a corresponding Sturmian theory and discuss methods of oscillation theory, which we use to present oscillation as well as nonoscillation criteria for halflinear dynamic equations.