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Vlasov, V. V.; Ivanov, S. A.

Sharp estimates for solutions of systems with aftereffect. (English. Russian original) Zbl 1206.34089

St. Petersbg. Math. J. 20, No. 2, 193-211 (2009); translation from Algebra Anal. 20, No. 2, 43-69 (2008).
Summary: Sharp estimates are established for strong solutions of systems of differential-difference equations of both neutral and retarded type. The approach is based on the study of the resolvent corresponding to the generator of the semigroup of shifts along the trajectories of a dynamical system. In the case of neutral type equations, the Riesz basis property of the subsystem of exponential solutions is used.

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MSC:

34K12 Growth, boundedness, comparison of solutions to functional-differential equations
34K06 Linear functional-differential equations
34K40 Neutral functional-differential equations
47A10 Spectrum, resolvent
47D06 One-parameter semigroups and linear evolution equations
47N20 Applications of operator theory to differential and integral equations

Keywords:

differential-difference equation; retarded type; neutral type; neutral-neutral type
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References:

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