Geodesic
Boundary-value problems for the one-dimensional \(p\)-Laplacian with even superlinearity
Electronic journal of differential equations, Tome 1999 (1999)
This paper is concerned with a study of the quasilinear problem $-(|u'|^{p-2}u')'= |u|^p-\lambda$, in (0,1) $u(0) =u(1) =0$, where $p greater than 1$ and $\lambda \in {\Bbb R}$ are parameters. For $\lambda$, we determine a lower bound for the number of solutions and establish their nodal properties. For $\lambda \leq 0$, we determine the exact number of solutions. In both cases we use a quadrature method.
Classification : 34B15, 34C10
Keywords: one-dimensional p-Laplacian, two-point boundary-value problem, superlinear, time mapping 
@article{EJDE_1999__1999__a94,
     author = {Addou,  Idris and Benmeza{\"\i},  Abdelhamid},
     title = {Boundary-value problems for the one-dimensional {\(p\)-Laplacian} with even superlinearity},
     journal = {Electronic journal of differential equations},
     year = {1999},
     volume = {1999},
     zbl = {0923.34024},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a94/}
}
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Addou,  Idris; Benmezaï,  Abdelhamid. Boundary-value problems for the one-dimensional \(p\)-Laplacian with even superlinearity. Electronic journal of differential equations, Tome 1999 (1999). http://geodesic.mathdoc.fr/item/EJDE_1999__1999__a94/