Nguyen Van Loi

EXISTENCE AND GLOBAL BIFURCATION OF PERIODIC SOLUTIONS TO A CLASS OF DIFFERENTIAL VARIATIONAL INEQUALITIES

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.

Decay solutions for a class of fractional differential variational inequalities

Abstract Our aim is to study a new class of differential variational inequalities involving fractional derivatives. Using the fixed point approach, the existence of decay solutions to the mentioned problem is proved.

An approximation solvability method for nonlocal differential problems in Hilbert spaces

A new approach is developed for the solvability of nonlocal problems in Hilbert spaces associated to nonlinear differential equations. It is based on a joint combination of the degree theory with the approximation solvability method and the bounding functions technique. No compactness or condensivity condition on the nonlinearities is assumed. Some applications of the abstract result to the study of nonlocal problems for integro-differential equations and systems of integro-differential equations are then showed. A generalization of the result by using nonsmooth bounding functions is given.

Nonlocal problem for differential complementarity systems

In this paper, by using the topological degree theory for multivalued maps and the bounding function method, we give sufficient conditions for the existence of solutions to a nonlocal problem of differential complementarity systems. An example is given.

Guiding functions for generalized periodic problems and applications

Abstract In this paper, developing the method of guiding functions for differential inclusions with a generalized periodic condition we obtain the existence theorem for such problems. It is shown how the abstract result can be applied to the study of differential games and anti-periodic problems.

Second-Order Differential Inclusions

Various aspects of the theory of second-order differential inclusions attract the attention of many researchers (see., e.g., [1, 2, 6, 12, 18, 42, 46, 47, 68, 70, 97]). In this chapter we consider the boundary value problem of form

Method of Guiding Functions in Finite-Dimensional Spaces

\displaystyle{ {u}^{{\prime\prime}}\in Q(u),\;\;u(0) = u(1) = 0, }

On controllability of Duffing equation

(4.1) for second-order differential inclusions which arises naturally from some physical and control problems. Using the method of guiding functions we study the existence of solutions of problem (4.1) in an one-dimensional and in Hilbert spaces.