Noncoercive hemivariational inequality approach to constrained problems for star-shaped admissible sets

Abstract

The hemivariational inequality approach is used in order to establish the existence of solutions to a large class of noncoercive constrained problems in a reflexive Banach space, in which the set of all admissible elements is not convex but fulfills some star-shaped property.

Coercive and Noncoercive Mixed Generalized Complementarity Problems

“…The recession function of Baocchi et al [19] was then extended by Goeleven [21] in 1996 to a general single-valued operator F from B to B * with respect to z 0 ∈ B as r z 0 ,F (x) := lim inf t→+∞ z→x…”

“…The recession function of Goeleven [21] was then further extended by Sahu, Chadli, Mohapatra, and Pani [23] in 2021 to the case of multivalued mappings as given below.…”

“…A bridge between the recession function and recession cone was established by Baiocchi et al [19] in 1988. Later on, the concept of recession functions, as well as recession cones, was enormously used by various authors while evaluating noncoercive equilibrium problems, as well as variational inequalities [20][21][22].…”

On the Hemivariational Inequality Approach to Nonconvex Constrained Problems in the Theory of von Kármán Plates

“…We refer to [9], [26] and [27] for more information concerning this class of operators. Let C c X be a nonempty closed subset.…”

On variational-hemivariational inequalities with nonconvex constraints

“…We consider the case where the constrained set is star-shaped with respect to a ball. Hemivariational inequalities with nonconvex constrained set were studied earlier for stationary problems by Naniewicz [8], Naniewicz and Panagiotopoulos [2, Section 7.4], Goeleven [9], and Goeleven [10] in a noncoercive framework. Evolutionary constrained problems on star-shaped sets were studied in [11,12].…”