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A multiplicity result for a perturbation of a symmetric Dirichlet problem. (English) Zbl 1122.35031
In the present study the author investigates the existence of at least three solutions for the following Dirichlet problem \[ -\Delta u= f(x,u)+\lambda g(x, u)\quad\text{a.e. in }\Omega, \] \[ u= 0\quad\text{on } \partial\Omega, \] where \(\Omega\subset\mathbb{R}^N\) is a bounded open set with sufficiently smooth boundary J\(\partial\Omega\), \(\lambda\in\mathbb{R}\) and \(f\), \(g\) are satisfies natural assumptions.

MSC:
35J60 Nonlinear elliptic equations
35J20 Variational methods for second-order elliptic equations
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