Abstract
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)>0,0<x<1,u(0)=u(1)=0, where λ>0 is a parameter and p,q satisfy 0<p<1<q<+∞. The arguments are based upon a time-map method.
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