In this paper, we investigate the existence of solutions for double-phase problems with variable exponents of the Kirchhoff–Schrödinger type, incorporating a convection term. By imposing certain assumptions and utilizing the topological degree for a class of (S+)-demicontinuous operators, along with the Galerkin method within the framework of Musielak–Orlicz–Sobolev spaces, we establish the existence of strong generalized solutions and weak solutions for the problems under consideration.

中文翻译：

---

关于一类具有对流项和可变指数的 Schrödinger-Kirchhoff 双相问题


在本文中，我们研究了具有 Kirchhoff-Schrödinger 型可变指数的双相问题的解，并结合了对流项。通过施加某些假设并利用一类 （S+） -半连续算子的拓扑度数，以及 Musielak-Orlicz-Sobolev 空间框架内的 Galerkin 方法，我们确定了所考虑的问题存在强广义解和弱解。