04-372 Alexandra Scheglova
The multiplicity of solutions for a boundary value problem with nonlinear Neumann condition (400K, pdf) Nov 9, 04
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Abstract. We prove the existence of any given number of nonequivalent solutions for the BVP $$ \left\{ \begin{array}{rcll} -\Delta_p u + |u|^{p-2}u&=&0 & \mbox{ in }B_R \\ |\nabla u|^{p-2}\langle\nabla u;{\bf n}\rangle &=& |u|^{q-2}u & \mbox{ on }S_R \end{array},\right. $$ 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 $p=2$.

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