Half-linear dynamic equations

• Autoři: AGARWAL Ravi P.; BOHNER Martin; ŘEHÁK Pavel
• Rok publikování: 2003
• Druh: Kapitola v knize
• Fakulta / Pracoviště MU: Pedagogická fakulta
• Popis: 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.

Související projekty

• Kvalitativní teorie pololineárních diferenciálních a diferenčních rovnic
• Kvalitativní teorie řešení diferenčních rovnic