Existence and Global Bifurcation of Periodic Solutions to a Class of Differential Variational Inequalities

Abstract

In this paper, by using the topological degree theory for multivalued maps and the method of guiding functions, the existence and global bifurcation for periodic solutions of a class of differential variational inequalities are studied.

A system of evolutionary problems driven by a system of hemivariational inequalities

“…A special case of (f1) is when f(t, x, ·) : K → E 1 is affine for all (t, x) ∈ [0, T ] × E. In Pang and Stewart [25] and Liu et al [17] it is utilized an f of the form f(t, x, u) = g(t, x) + B(t, x)u.…”

“…It is worth to point out that the aspects related to problem (EEVI), have been until now examined only in a finite dimensional content when E = R n , E 1 = R m , A = 0 (see Gwinner [9,10], Li et al [14], and Pang and Stewart [25]). Liu et al [17] devoted to the case E = R n , E 1 = R m , A = 0, and f(t, x(t), u(t)) = g(t, x(t)) + B(t, x(t))u(t). Actually, in these works an ordinary differential equation is parameterized by an algebraic variable required to solve a finite-dimensional variational inequality in the state variable of the differential equation.…”

A class of fractional differential hemivariational inequalities with application to contact problem

“…Since then, many scientists have contributed to the development of (DVI). In 2013 Liu et al [24] employed the topological degree theory for multivalued maps and the method of guiding functions to establish the existence and global bifurcation behavior for periodic solutions to a class of differential variational inequalities in finite-dimensional spaces. In 2014 Chen and Wang [8], using the idea of (DVI), have solved the dynamic Nash equilibrium problem with shared constraints, which involves a dynamic decision process with multiple players.…”

“…Note that since the contact process is assumed to be quasistatic, the acceleration term is negligible and we deal in Q with equilibrium equation (23), where f 0 denotes the time dependent density of volume forces. Moreover, conditions (24) and (25) reveal the displacement and traction boundary conditions on parts Γ D and Γ N of the boundary, respectively, i.e., the body is fixed on Γ D and it is subjected to the time dependent surface traction of density f N on Γ N .…”

Nonlinear evolutionary systems driven by quasi‐hemivariational inequalities

“…This notion arises in many applied problems such as electrical circuits with ideal diodes, Coulomb friction for contacting bodies, economical dynamics, dynamic traffic networks. () Among the results dealing with this type of problems, we mention that of Liu et al studying the global bifurcation of periodic solutions for …”