Geodesic
A fibering map approach to a semilinear elliptic boundary value problem
Electronic journal of differential equations, Tome 2007 (2007)
We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem

$ -\Delta u(x) = \lambda a(x) u^q + b(x) u^p \quad\hbox{for } x \in \Omega; \quad u(x) = 0 \quad \hbox{for } x \in \partial \Omega $

on a bounded region $\Omega$ by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs.
Classification : 35J20, 36J65
Keywords: semilinear elliptic boundary value problem, variational methods, Nehari manifold, fibering map 
@article{EJDE_2007__2007__a271,
     author = {Brown,  Kenneth J. and Wu,  Tsung-Fang},
     title = {A fibering map approach to a semilinear elliptic boundary value problem},
     journal = {Electronic journal of differential equations},
     year = {2007},
     volume = {2007},
     zbl = {1133.35337},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a271/}
}
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%A Wu,  Tsung-Fang
%T A fibering map approach to a semilinear elliptic boundary value problem
%J Electronic journal of differential equations
%D 2007
%V 2007
%U http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a271/
%G en
%F EJDE_2007__2007__a271
Brown,  Kenneth J.; Wu,  Tsung-Fang. A fibering map approach to a semilinear elliptic boundary value problem. Electronic journal of differential equations, Tome 2007 (2007). http://geodesic.mathdoc.fr/item/EJDE_2007__2007__a271/