Controllability of mild solutions for second-order neutral evolution equations with state-dependent delay. (English) Zbl 07849474
Summary: The objective of our research is to demonstrate the controllability of mild solutions for a specific class of second-order neutral functional evolution equations that involve state-dependent delay. To achieve this, we rely on Avramescu’s nonlinear alternative theorem and leverage cosine function theory.
MSC:
| 03C85 | Second- and higher-order model theory |
| 34G20 | Nonlinear differential equations in abstract spaces |
| 34K40 | Neutral functional-differential equations |
| 37L05 | General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations |
| 47D09 | Operator sine and cosine functions and higher-order Cauchy problems |
| 47H10 | Fixed-point theorems |
| 93B05 | Controllability |
Keywords:
second order evolution equations; neutral problem; controllability; state-dependent delay; nonlinear alternative; cosine function of operatorsReferences:
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