Geodesic
Multiplicity results for classes of one-dimensional \(p\)-Laplacian boundary-value problems with cubic-like nonlinearities
Electronic journal of differential equations, Tome 2000 (2000)
We study boundary-value problems of the type

$\displaylines{ -(\varphi_{p}( u') ) ' =\lambda f( u) ,\hbox{ in }(0,1) \cr u( 0) =u( 1) =0, }$

where p>1, $\varphi_{p}( x) =\left| x\right| ^{p-2}x$, and $\lambda$ is positive. We provide multiplicity results when f behaves like a cubic with three distinct roots, at which it satisfies Lipschitz-type conditions involving a parameter q>1. We shall show how changes in the position of q with respect to p lead to different behavior of the solution set. When dealing with sign-changing solutions, we assume that f is half-odd; a condition generalizing the usual oddness. We use a quadrature method.
Classification : 34B15
Keywords: p-Laplacian, time-maps, multiplicity results, cubic-like nonlinearities 
@article{EJDE_2000__2000__a139,
     author = {Addou,  Idris},
     title = {Multiplicity results for classes of one-dimensional {\(p\)-Laplacian} boundary-value problems with cubic-like nonlinearities},
     journal = {Electronic journal of differential equations},
     year = {2000},
     volume = {2000},
     zbl = {0952.34007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a139/}
}
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JO  - Electronic journal of differential equations
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%A Addou,  Idris
%T Multiplicity results for classes of one-dimensional \(p\)-Laplacian boundary-value problems with cubic-like nonlinearities
%J Electronic journal of differential equations
%D 2000
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Addou,  Idris. Multiplicity results for classes of one-dimensional \(p\)-Laplacian boundary-value problems with cubic-like nonlinearities. Electronic journal of differential equations, Tome 2000 (2000). http://geodesic.mathdoc.fr/item/EJDE_2000__2000__a139/