TY  - JOUR
ID  - Cherepennikov2006
LB  - Cherepennikov2006
AU  - Cherepennikov, Valery B.
AU  - Ermolaeva, Polina G.
TI  - Polynomial quasisolutions of linear differential-difference equations
ST  - Polynomial quasisolutions of linear differential-difference equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 3
SP  - 431
EP  - 443
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.3.431
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.3.431
AB  - The paper discusses a linear differential-difference equation of neutral type with linear coefficients, when at the initial time moment \(t=0\) the value of the desired function \(x(t)\) is known. The authors are not familiar with any results which would state the solvability conditions for the given problem in the class of analytical functions. A polynomial of some degree \(N\) is introduced into the investigation. Then the term "polynomial quasisolution" (PQ-solution) is understood in the sense of appearance of the residual \(\Delta (t)=O(t^N)\), when this polynomial is substituted into the initial problem. The paper is devoted to finding PQ-solutions for the initial-value problem under analysis.
KW  - differential-difference equations
KW  - neutral type
KW  - initial value problem
KW  - polynomial quasisolution
SN  - 1232-9274
ER  -