Three solutions for a Neumann problem

Biagio Ricceri

DOI: http://dx.doi.org/10.12775/TMNA.2002.037

Abstract


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 $\varrho$.

Keywords


Minimax inequality; multiplicity

Full Text:

FULL TEXT

Refbacks

  • There are currently no refbacks.

Partnerzy platformy czasopism