Three solutions for a Neumann problem
Keywords
Minimax inequality, multiplicityAbstract
In this paper we consider a Neumann problem of the type $$ \cases -\Delta u = \alpha (x) (\vert u\vert^{q-2}u-u)+\lambda f(x,u) &\text{in } \Omega, \\ \displaystyle {\partial u\over \partial \nu}=0 &\text{on } \partial\Omega. \endcases \tag \hbox{$\text{\rm P}_{\lambda}$} $$ Applying the theory developed in [< i> On a three critical points theorem< /i> , Arch. Math. (Basel) < b> 75< /b> (2000), 220–226], we establish, under suitable assumptions, the existence of an open interval $\Lambda\subseteq \mathbb R$ and of a positive real number $\varrho$, such that, for each $\lambda\in\Lambda$, problem (P$_{\lambda}$) admits at least three weak solutions in $W^{1,2}(\Omega)$ whose norms are less than $\varrho$.Downloads
Published
2002-12-01
How to Cite
1.
RICCERI, Biagio. Three solutions for a Neumann problem. Topological Methods in Nonlinear Analysis. Online. 1 December 2002. Vol. 20, no. 2, pp. 275 - 281. [Accessed 19 April 2024].
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