D-stability of the model of the Stieltjes string related to the functional differential equations

Abstract

The following model p(t)u′(t)−p(0)β−∫0t((gu)(s)+∑i=1m(ξi(s)x(νi(s))−ψi(s)x(μi(s))))dQ(s)=−F(t)of the Stieltjes string on the segment [0,l]with a nonlocal initial value condition u(0)=αis considered. D-stability conditions of the unique solution of the mentioned problem are established. Also, example is presented.

Keywords

• Stieltjes string
• Nonlocal initial value condition
• Lebesgue–Stieltjes integral
• Measurable function
• D-stability