We consider the existence of at least one positive radially symmetric solution to a class of nonlocal quasilinear PDEs having the form \(\begin{aligned} -A\left( \int _{{\mathcal {B}}_1}g\big (u(\varvec{s})\big )~{\textrm{d}}\varvec{s}\right) \Delta _pu=\lambda f\big (|\varvec{x}|,u(\varvec{x})\big ), \quad \varvec{x}\in {\mathcal {B}}_1 \end{aligned}\) subject to the Dirichlet boundary data \(u(\varvec{x})=0,\) \(\varvec{x}\in \partial {\mathcal {B}}_1,\) where \({\mathcal {B}}_1\) is the unit ball in \({\mathbb {R}}^{n};\) here A is a function that captures the nonlocal aspect of the problem. As part of our analysis, we also consider existence of at least one positive solution to the one-dimensional nonlocal p-Laplacian equation \(\begin{aligned} -A\left( \big (a*(g\circ u)\big )(1)\right) \big (\varphi _p\circ u'\big )'(t)=\lambda f\big (t,u(t)\big ),\quad 0<t<1, \end{aligned}\) subject to the left-focal boundary data \(\begin{aligned} u'(0)=0\quad \text {and}\quad u(1)=0. \end{aligned}\) Our methodology involves topological fixed point theory. Of special note is that we must analyze a modified problem, which involves a truncation of the forcing term f. This unusual aspect is due to the p-Laplacian operator occurring in the differential equations.
