Opuscula Math.
26
, no. 3
(), 431-443
Opuscula Mathematica

# Polynomial quasisolutions of linear differential-difference equations

Abstract. 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.
Keywords: differential-difference equations, neutral type, initial value problem, polynomial quasisolution.
Mathematics Subject Classification: 34K15.