We consider nonlocal differential equations with convolution coefficients of the form
−
M
(
(
a
∗
u
q
)
(
1
)
)
u
(
t
)
=
λ
f
(
t
,
u
(
t
)
)
,
t
∈
(
0
,
1
)
,
\begin{equation} -M\Big (\big (a*u^q\big )(1)\Big )u(t)=\lambda f\big (t,u(t)\big ),t\in (0,1),\notag \end{equation}
and we demonstrate an explicit range of
λ
\lambda
for which this problem, subject to given boundary data, will not admit a nontrivial positive solution; if
a
≡
1
a\equiv 1
, then the model case
−
M
(
‖
u
‖
L
q
(
0
,
1
)
q
)
u
(
t
)
=
λ
f
(
t
,
u
(
t
)
)
,
t
∈
(
0
,
1
)
\begin{equation} -M\Big (\Vert u\Vert _{L^q(0,1)}^{q}\Big )u(t)=\lambda f\big (t,u(t)\big ),t\in (0,1)\notag \end{equation}
is obtained. The range of
λ
\lambda
is calculable in terms of initial data, and our results allow for a variety of kernels,
a
a
, to be utilized, including, for example, those leading to a fractional integral coefficient of Riemann-Liouville type. Two examples are provided in order to illustrate the application of the result.