We consider an elliptic boundary-value problem with a homogeneous Dirichlet boundary condition, a parameter and a discontinuous non-linearity. The positive parameter appears as a multiplicative term in the non-linearity, and the problem has a zero solution for any value of the parameter. The non-linearity has superlinear growth at infinity. We prove the existence of positive solutions by a topological method.

中文翻译：

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具有不连续非线性的超线性椭圆问题的正解

我们考虑具有齐次狄利克雷边界条件、参数和不连续非线性的椭圆边值问题。正参数在非线性中表现为乘法项，对于该参数的任何值，问题都有零解。非线性在无穷远处具有超线性增长。我们通过拓扑方法证明了正解的存在。