We discuss the multiplicity of nonnegative solutions of a parametric one-dimensional mean curvature problem. Our main e ort here is to describe the configuration of the limits of a certain function, depending on the potential at zero, that yield, for certain values of the parameter, the existence of infinitely many weak nonnegative and nontrivial solutions. Moreover, thanks to a classical regularity result due to Lieberman, this sequence of solutions strongly converges to zero in C1([0; 1]). Our approach is based on recent variational methods.
