Functional Differential Equations

Front Matter....Pages i-ix
Introduction....Pages 1-10
A General Initial Value Problem....Pages 11-12
Existence....Pages 13-15
Continuation of Solutions....Pages 16-20
Continuous Dependence and Uniqueness....Pages 21-23
Backward Continuation....Pages 24-29
Caratheodory Conditions....Pages 30-31
Remarks on the Map Defined by Solutions....Pages 32-42
Autonomous Systems....Pages 43-46
Definitions of Stability....Pages 47-50
Sufficient Conditions for Stability of General Systems....Pages 51-64
Sufficient Conditions for Instability....Pages 65-68
Stability in Autonomous Systems....Pages 69-71
An Example of Levin and Nohel....Pages 72-77
An Equation of Volterra....Pages 78-79
Nonhomogeneous Linear Systems....Pages 80-87
The “Adjoint” Equation and Representation of Solutions....Pages 88-90
Stability of Perturbed Systems....Pages 91-93
Linear Autonomous Equations. The Semigroup and Infinitesimal Generator....Pages 94-97
The Eigenvalues of a Linear Autonomous Equation. Decomposition of C.....Pages 98-103
Decomposing C with the Adjoint Equation....Pages 104-111
Estimates on the Complementary Subspace....Pages 112-115
An Example....Pages 116-119
The Decomposition in the Variation of Constants Formula....Pages 120-124
Forced Linear Systems....Pages 125-130
The Saddle Point Property....Pages 131-141
A Fixed Point Theorem for Cones....Pages 142-151
A Periodicity Theorem for Functional Equations....Pages 152-155
The Equation $${\rm{\dot x}}\left( {\rm{t}} \right) = - \alpha {\rm{x}}\left( {{\rm{t}} - 1} \right)\left[ {{\rm{1}} + {\rm{x}}\left( {\rm{t}} \right)} \right]$$ ....Pages 156-161
The Equation $${\rm{\dot x}}\left( {\rm{t}} \right) = - \alpha {\rm{x}}\left( {{\rm{t}} - 1} \right)\left[ {{\rm{l}} - {\rm{x}}^2 \left( {\rm{t}} \right)} \right]$$ ....Pages 162-163
The Equation $${\rm{\ddot x}}\left( {\rm{t}} \right) + {\rm{f}}\left( {{\rm{x}}\left( {\rm{t}} \right){\rm{\dot x}}\left( {\rm{t}} \right)} \right) + {\rm{g}}\left( {{\rm{x}}\left( {{\rm{t}} - {\rm{r}}} \right)} \right) = 0$$ ....Pages 164-176
The “Adjoint” Equation for General Linear Systems....Pages 177-181
The True Adjoint of a Linear System....Pages 182-186
Boundary Value Problems....Pages 187-195
Linear Periodic Systems. General Theory....Pages 196-202
Decomposition of Linear Periodic Systems....Pages 203-212
Nondegenerate Periodic Orbits....Pages 213-220
Notes and Remarks....Pages 221-226
Back Matter....Pages 227-239