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Existence et multiplicité des solutions d’un problème aux valeurs propres elliptique semilinéaire. (Existence and multiplicity of solutions to a semilinear elliptic eigenvalue problem). (French) Zbl 0606.35035
In this note we study the problem \[ -\Delta u=\lambda f(u)\quad in\quad \Omega,\quad \lambda >0;\quad u=0\quad on\quad \partial \Omega, \] where \(\Omega\) is a bounded domain of \({\mathbb{R}}^ N\) and f possesses at least two zeros.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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