Alexandra Scheglova
The multiplicity of solutions for a boundary value problem with nonlinear Neumann condition
(400K, pdf)

ABSTRACT.  We prove the existence of any given number of nonequivalent solutions for the 
BVP 
$$
\left\{ \begin{array}{rcll}
-\Delta_p u + |u|^{p-2}u&=&0 & \mbox{ in }B_R \\
|\nabla u|^{p-2}\langle\nabla u;{\bf n}\rangle &=& |u|^{q-2}u &
\mbox{ on }S_R 
\end{array},\right.
$$
under some conditions on $q$ and $R$. Nonradial solutions are constructed 
also for $[(n+1)/2]+1\le p<n$ and some supercritical $q$. The most part of 
results is new even in the case $p=2$.