Exponential dichotomy and stability of neutral type equations
The authors study the linear functional differential equation of neutral type with unbounded delay (1) \(Lx=(d/ds)Dx+Bx=0\) where D, B are linear bounded retarded operators with exponentially fading memory. If L is understood as an operator from C into the special space \(C^{-1}\) of distributions, then its invertibility is equivalent to the presence of exponential dichotomy of the solutions of (1). The theory is applied to prove theorems on stability and instability in the first approximation for neutral functional differential equations of a general form.
linear functional differential equation of neutral type with unbounded delay
neutral functional differential equations
scientific article; zbMATH DE number 4086131
scientific article