The authors study the problem - ∆u + \lambda u = u^{p-1} in Ω u > 0 in Ω with Neumann boundary conditions. Here Ω is a smooth bounded domain in R^N, N≥3, and p>2 is subcritical. They show that this problem has at least cat(Ω)+1 solutions if $\lambda$ is sufficiently large. The key idea is to show, by a concentration analysis argument, that low energy sublevels of an associated functional inherit the topology of Ω if $\lambda$ is large.
The role of the boundary in some semilinear Neumann problems
Musina, Roberta
1992-01-01
Abstract
The authors study the problem - ∆u + \lambda u = u^{p-1} in Ω u > 0 in Ω with Neumann boundary conditions. Here Ω is a smooth bounded domain in R^N, N≥3, and p>2 is subcritical. They show that this problem has at least cat(Ω)+1 solutions if $\lambda$ is sufficiently large. The key idea is to show, by a concentration analysis argument, that low energy sublevels of an associated functional inherit the topology of Ω if $\lambda$ is large.File in questo prodotto:
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