We use asymptotic analysis and generalized asymptotic functions for studying nonlinear and noncoercive mixed variational inequalities in finite dimensional spaces in the nonconvex case, that is, when the operator is nonlinear and noncoercive and the function is nonconvex and noncoercive. We provide general necessary and sufficient optimality conditions for the set of solutions to be nonempty and compact. As a consequence, a characterization of the nonemptiness and compactness of the solution set, when the operator is affine and the function is convex, is given. Finally, a comparison with existence results for equilibrium problems is presented.

中文翻译：

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关于“有限维空间中非强制性混合变分不等式的存在结果”的注解

我们使用渐近分析和广义渐近函数来研究非凸情况下有限维空间中的非线性和非强制混合变分不等式，即当算子为非线性非强制且函数为非凸非强制时。我们为非空且紧致的解决方案集提供了一般必要和充分的最优性条件。因此，给出了当算子为仿射函数且函数为凸函数时解集的非空性和紧致性的表征。最后，对平衡问题的存在结果进行了比较。