Research Information System
Applicable Analysis, vol.105, no.7, pp.1542-1563, 2026 (SCI-Expanded, Scopus)
In this paper, we investigate a class of multidimensional semi-infinite variational inequality problems and analyze their well-posedness by examining the distance between approximate and exact solutions and the strict monotonicity of the functional. Further, we use the monotonicity and hemicontinuity of the real-valued functional to investigate both the well-posedness and the well-posedness in the generalized sense of the semi-infinite variational inequality problems. Moreover, we formulate a gap function for multidimensional semi-infinite variational inequality problems and establish a relationship between the well-posedness of the aforementioned variational inequality problem and its corresponding gap function. In addition, we present a water distribution problem, where a municipality aims to minimize the cost of supplying water as an illustrative example to demonstrate the validity and applicability of the theoretical results.