Abstract
Our aim in this paper is to investigate the existence and uniqueness result for a class of mixed variational problems. They are governed by two variational inequalities. By applying the saddle-point theory, we obtain the existence of solutions to mixed variational problems. Finally, some frictional contact problems are given to illustrate our main results.
Highlights
1 Introduction The abstract problem in this paper is a class of mixed variational problems governed by two variational inequalities, with a bilinear function and functional which is convex and lower semicontinuous
The purpose of this paper is to investigate the weak solvability of a unilateral frictionless contact problem using a technique with dual Lagrange multipliers
5 Conclusion In this paper, we study a class of mixed variational problems governed by two variational inequalities with dual Lagrange multipliers
Summary
The abstract problem in this paper is a class of mixed variational problems governed by two variational inequalities, with a bilinear function and functional which is convex and lower semicontinuous. Considering such kinds of variational problems sets the functional background in the study of elastic contact problems with unilateral constraints and nonmonotone interface laws. Let X be a Hilbert space, Y a reflexive Banach space and be a nonempty, closed and convex subset Y. Let A : X → X, B : X × → R, φ : X → R be given maps to be specified later, and w, f ∈ X be fixed.
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