Solvability of autonomous differential equation with aftereffect on negative semi-axis

A. S. Balandin ; T. L. Sabatulina

Izvestiâ vysših učebnyh zavedenij. Matematika, no. 10 (2017), pp. 26-37.

Résumé

We consider a linear autonomous homogeneous functional differential equation on the real negative semi-axis. We prove that if solutions belong to the special space of functions with integral limitations, then the space of solutions is finite-dimensional and its basis is formed by the solutions of the form $(t^m\exp(pt))$ generated by the roots of the characteristic equation. In contrast to the spaces used earlier, the pointwise estimation of solutions is replaced by the integral one. We adduce examples of differential equations with aftereffect and give the effective description of the space of solutions for these equations.

Détail

Keywords: functional differential equation, aftereffect, solvability on the axis, space of functions with exponential weight.

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