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Zbl 0970.35089
Ricceri, B.
Existence of three solutions for a class of elliptic eigenvalue problems.
(English)
[J] Math. Comput. Modelling 32, No.11-13, 1485-1494 (2000). ISSN 0895-7177

The author considers the problem $-\Delta u = \lambda(f(u)+\mu g(u))$ in $\Omega$, $u|_{\partial\Omega}=0$, $\Omega\subset\Bbb R^n$, $f$ and $g$ are continuous functions. It is shown, under suitable conditions, the existence of at least three solutions for some $\lambda>0$, if $|\mu|$ is small enough. The abstract scheme which is corresponding to this problem is a novelty: it is not reducible to the Landesman--Lazer or Ambrosetti-- Rabinowitz methods.
[Serghey G.Suvorov (Donetsk)]
MSC 2000:
*35P30 Nonlinear eigenvalue problems for PD operators
47J30 Variational methods
58E99 Variational problems in infinite-dimensional spaces

Keywords: nonlinear eigenvalue problems; local minima; multifunctions; minimax inequalities

Cited in: Zbl 1150.34342 Zbl 1146.35364

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