On a boundary value problem for integro-differential equations on the halfline Original Research Article

The following boundary value problem equation(0.1) View the MathML sourcex′(t)=p(t)∫0σ(t)q(s)x(τ(s))ds, Turn MathJax on equation(0.2) View the MathML sourcex(t)=φ(t)fort∈[τ0,0),lim inft→+∞|x(t)|<+∞ Turn MathJax on is considered, where p∈C(R+;(0,+∞))p∈C(R+;(0,+∞)), q∈Lloc(R+;R+)q∈Lloc(R+;R+), 0≤σ(t)≤t0≤σ(t)≤t, τ(t)