One-dimensional elliptic equation with concave and convex nonlinearities

Abstract

We establish the exact number of positive solutions for the boundary-value problem $$displaylines{ -(|u'|^{m-2} u')'=lambda u^q + u^pquad hbox{in }(0,1)cr u(0)= u(1)=0,, }$$ where $0leq q < m- 1 < p$ and $lambda$ is positive.

Keywords

• m-Laplacian
• concave-convex nonlinearities
• exactness results
• time-maps.