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dc.contributor.authorWinter, M-
dc.contributor.authorGui, C-
dc.contributor.authorWei, J-
dc.identifier.citationAnn Inst Henri Poincare Anal Nonl. 17(2000): 47-82en
dc.description.abstractWe consider the problem \left \{ \begin{array}{rcl} \varepsilon^2 \Delta u - u + f(u) = 0 & \mbox{ in }& \ \Omega\\ u > 0 \ \mbox{ in} \ \Omega, \ \frac{\partial u}{\partial \nu} = 0 & \mbox{ on }& \ \partial\Omega, \end{array} \right. where \Omega is a bounded smooth domain in R^N, \varepsilon>$ is a small parameter and f is a superlinear, subcritical nonlinearity. It is known that this equation possesses boundary spike solutions such that the spike concentrates, as \varepsilon approaches zero, at a critical point of the mean curvature function H(P), P \in \partial \Omega . It is also known that this equation has multiple boundary spike solutions at multiple nondegenerate critical points of H(P) or multiple local maximum points of H(P). In this paper, we prove that for any fixed positive integer $K$ there exist boundary $K-peak$ solutions at a local minimum point of $H(P)$. This implies that for any smooth and bounded domain there always exist boundary $K-peak$ solutions. We first use the Liapunov-Schmidt method to reduce the problem to finite dimensions. Then we use a maximizing procedure to obtain multiple boundary spikes.en
dc.format.extent263500 bytes-
dc.subjectMultiple boundary spikesen
dc.subjectNonlinear elliptic equationsen
dc.titleMultiple boundary peak solutions for some singularly perturbed Neumann problemsen
dc.typeResearch Paperen
Appears in Collections:Dept of Mathematics Research Papers
Mathematical Sciences

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