Half-linear dynamic equations

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Authors

AGARWAL Ravi P. BOHNER Martin ŘEHÁK Pavel

Year of publication 2003
Type Chapter of a book
MU Faculty or unit

Faculty of Education

Citation
Description We survey half-linear dynamic equations on time scales. These contain the well-known half-linear differential and half-linear difference equations as special cases, but also other kinds of half-linear equations. Special cases of half-linear equations are the well-studied 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 half-linear dynamic equations, among them solvability of an associated Riccati equation and positive definiteness 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 half-linear dynamic equations.
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