Exact number of solutions of a one-dimensional prescribed mean curvature equation with concave-convex nonlinearities

In this paper, an exact number of solutions is obtained for the one-dimensional prescribed mean curvature equation with concave-convex nonlinearities in the form of {−(u′1+u′2)′=λ(up+uq),u(x)>0,00 is a parameter and p,q satisfy 0