The author considers a class of nonlocal convolution-type ordinary differential equations the form − A ∗ ( g ∘ u ) 1 ′ t = λ f , 0 < $$\begin{equation*} \quad -A{\left({\left(a*(g\,\circ\, u)\right)}(1)\right)}u^{\prime \prime }(t)=\lambda f{\left(t,u(t)\right)}, 1,\nonumber \end{equation*}$$ where $g$ is continuous function satisfying p q $(p,q)$ growth — that is, there exist constants c $c_1$...