Electron. J. Diff. Eqns., Vol. 2000(2000), No. 50, pp. 1-9.

One-dimensional elliptic equation with concave and convex nonlinearities

Justino Sanchez & Pedro Ubilla

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

Submitted February 1, 2000. Published June 25, 2000.
Math Subject Classifications: 34B15.
Key Words: m-Laplacian, concave-convex nonlinearities, exactness results, time-maps.

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Justino Sanchez
Universidad de Santiago de Chile
Casilla 307, Correo 2, Santiago, Chile
Pedro Ubilla
Universidad de Santiago de Chile
Casilla 307, Correo 2, Santiago, Chile
e-mail: pubilla@fermat.usach.cl

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