Electronic Journal of Differential Equations,
Vol. 1998(1998), No. 10, pp. 1-13.

Title: Existence and multiplicity of solutions to a  p-Laplacian
       equation with nonlinear boundary condition 

Author: Klaus Pflueger (Freie Univ. Berlin, Germany)

Abstract: 
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.

Submitted March 5, 1998. Published April 10, 1998.
Math Subject Classification: 35J65, 35J20.
Key Words: p-Laplacian; nonlinear boundary condition; variational methods;
           unbounded domain; weighted function space.