Geodesic
Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities
Electronic journal of differential equations, Tome 2000 (2000)
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},
     year = {2000},
     volume = {2000},
     zbl = {0942.34019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a8/}
}
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%A Addou,  Idris
%T Exact multiplicity results for quasilinear boundary-value problems with cubic-like nonlinearities
%J Electronic journal of differential equations
%D 2000
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%U 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/