Abstract We discuss, by topological methods, the solvability of systems of second-order elliptic differential equations subject to functional boundary conditions under the presence of gradient terms in the nonlinearities. We prove the existence of nonnegative solutions and provide a non-existence result. We present some examples to illustrate the applicability of the existence and non-existence results.

中文翻译：

---

具有梯度依赖和泛函 BC 的椭圆系统的非零正解

摘要 我们通过拓扑方法讨论了非线性中存在梯度项的情况下，受函数边界条件约束的二阶椭圆微分方程组的可解性。我们证明了非负解的存在并提供了一个不存在的结果。我们提供了一些例子来说明存在和不存在结果的适用性。