We prove existence of two solutions for an elliptic equation with exponential growth on a bounded domain. The first solution is obtained by an approximation scheme together with a fixed point theorem. The second solution is found by variational methods, and its expression is given by the sum of the first solution by other adequate function. The nonlinearities may have subcritical, critical or supercritical exponential growth.

中文翻译：

---

具指数增长的椭圆型方程的多解性。

我们证明了在有界域上具有指数增长的椭圆方程的两个解的存在性。第一种解决方案是通过逼近方案与不动点定理一起获得的。第二个解决方案是通过变分方法找到的，其表达式由第一个解决方案的和与其他适当函数的和给出。非线性可能具有亚临界，临界或超临界指数增长。