Dirichlet problem with indefinite nonlinearities

Abstract.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.

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