Dirichlet problem with indefinite nonlinearities
- Cite this article as:
- Chang, KC. & Jiang, MY. Cal Var (2004) 20: 257. doi:10.1007/s00526-003-0236-7
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We consider the following nonlinear elliptic equation \( -\triangle u -\lambda u = h_-(x) g_1(u) + h_ + (x) g_2(u) \) in a bounded domain \(\Omega\) with the Dirichlet boundary condition, \(h_-\le 0\) and \(h_ + \ge 0\), g1(u)u and g2(u)u are positive for |u| > > 1. Some existence results are given for superlinear g1 and g2 via the Morse theory.