 04372 Alexandra Scheglova
 The multiplicity of solutions for a boundary value problem with nonlinear Neumann condition
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Nov 9, 04

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Abstract. We prove the existence of any given number of nonequivalent solutions for the
BVP
$$
\left\{ \begin{array}{rcll}
\Delta_p u + u^{p2}u&=&0 & \mbox{ in }B_R \\
\nabla u^{p2}\langle\nabla u;{\bf n}\rangle &=& u^{q2}u &
\mbox{ on }S_R
\end{array},\right.
$$
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 $p=2$.
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