Geodesic
One-dimensional elliptic equation with concave and convex nonlinearities
Electronic Journal of Differential Equations, Tome 2000 (2000).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34B15
Keywords: m-Laplacian, concave-convex nonlinearities, exactness results, time-maps 
@article{EJDE_2000__2000__a11,
     author = {S\'anchez, Justino and Ubilla, Pedro},
     title = {One-dimensional elliptic equation with concave and convex nonlinearities},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a11/}
}
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Sánchez, Justino; Ubilla, Pedro. One-dimensional elliptic equation with concave and convex nonlinearities. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a11/