Geodesic
Existence and multiplicity of solutions to a $p$-Laplacian equation with nonlinear boundary condition
Electronic Journal of Differential Equations, Tome 1998 (1998).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study the nonlinear elliptic boundary value problem $$ A u = f(x,u) \quad {\rm in }\ \Omega\,,$ $ Bu = g(x,u) \quad {\rm on }\ \partial \Omega\,, where A is an operator of p-Laplacian type, $\Omega$ is an unbounded domain in ${\Bbb R}^N$ with non-compact boundary, and f and g are subcritical nonlinearities. We show existence of a nontrivial nonnegative weak solution when both f and g are superlinear. Also we show existence of at least two nonnegative solutions when one of the two functions f, g is sublinear and the other one superlinear. The proofs are based on variational methods applied to weighted function spaces.$$
Classification : 35J65, 35J20
Keywords: p-Laplacian, nonlinear boundary condition, variational methods, unbounded domain, weighted function space 
@article{EJDE_1998__1998__a35,
     author = {Pfl\"uger, Klaus},
     title = {Existence and multiplicity of solutions to a $p${-Laplacian} equation with nonlinear boundary condition},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a35/}
}
TY  - JOUR
AU  - Pflüger, Klaus
TI  - Existence and multiplicity of solutions to a $p$-Laplacian equation with nonlinear boundary condition
JO  - Electronic Journal of Differential Equations
PY  - 1998
VL  - 1998
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a35/
LA  - en
ID  - EJDE_1998__1998__a35
ER  - 
%0 Journal Article
%A Pflüger, Klaus
%T Existence and multiplicity of solutions to a $p$-Laplacian equation with nonlinear boundary condition
%J Electronic Journal of Differential Equations
%D 1998
%V 1998
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a35/
%G en
%F EJDE_1998__1998__a35
Pflüger, Klaus. Existence and multiplicity of solutions to a $p$-Laplacian equation with nonlinear boundary condition. Electronic Journal of Differential Equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a35/