In this work, we investigate the second-order nonlinear elliptic system defined on an unbounded domain and with variable nonconstant coefficients. We establish the existence of the solution of the nonlinear problem for a second-order nonstrongly elliptic system by using a coercive estimate, which is obtained for the linear case. The nonlinear elliptic system is transformed into an equivalent fixed point problem for a suitable nonlinear operator in a convex subset of a Banach function space. Using the topological fixed-point approach and embedding theorems, the conditions for solvability of the semiperiodical nonlinear problem in a weighted Sobolev space are obtained.

中文翻译：

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一类二阶非强椭圆系统的非线性问题的可解性

在这项工作中，我们研究了在无界域上定义的具有可变非恒定系数的二阶非线性椭圆系统。通过使用在线性情况下获得的强制估计，我们建立了二阶非强椭圆系统非线性问题解的存在性。对于Banach函数空间的凸子集中的合适的非线性算子，非线性椭圆系统转化为等效的不动点问题。使用拓扑定点方法和嵌入定理，获得了加权Sobolev空间中半周期非线性问题的可解条件。