Geodesic
Exact multiplicity results for quasilinear boundary-value problems with cubic-like 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 consider the boundary-value problem $-(\varphi_p (u'))' =\lambda f(u)$ in (0,1) $u(0) = u(1) =0$ where p> 1, $\lambda$ and $\varphi_p (x) =| x|^{p-2}x$. The nonlinearity $f$ is cubic-like with three distinct roots 0=a b c. By means of a quadrature method, we provide the exact number of solutions for all $\lambda$. This way we extend a recent result, for $p=2$, by Korman et al. [17] to the general case $p>1$. We shall prove that when $\1$p=$2 by Korman et al. [17], and strictly different in the case $p>2$.$
Classification : 34B15
Keywords: one dimensional p-Laplacian, multiplicity results, time-maps 
@article{EJDE_2000__2000__a8,
     author = {Addou, Idris},
     title = {Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2000},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a8/}
}
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Addou, Idris. Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities. Electronic Journal of Differential Equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a8/