Necessary and Sufficient Conditions for Oscillations of the Generalized Liénard Systems

In this paper, we study the second-order nonlinear differential systems of Liénard-type x˙=1a(x)[ h(y)−F(x) ], y˙=−a(x)g(x). Necessary and sufficient conditions to ensure that all nontrivial solutions are oscillatory are established by using a new nonlinear integral inequality. Our results substantially extend and improve previous results known in the literature.

SYSTEM OF GENERALIZED VECTOR VARIATIONAL INEQUALITIES

In this paper, the authors introduce and study system of generalized vector variational inequalities. Under suitable conditions, the existence of solutions for system of generalized vector variational inequalities is presented by Kakutani-Fan-Glicksberg fixed point theorem.

A new system of nonlinear variational inequalities with relaxed cocoercive mappings in reflexive Banach spaces

A new system for relaxed cocoercive non-linear variational inequalities in uniformly smooth Banach spaces is introduced and studied using the convergence of projection methods.Our results generalize and improve the corresponding results of recent works.

An Existence Theorem of Solutions for the System of Generalized Vector Quasi-Variational-Like Inequalities

In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces, which include the system of vector quasi-variational-like inequalities, the system of vector variational-like inequalities, the system of vector quasi-variational inequalities, and several other systems as special cases. Moreover, a number of C-diagonal quasiconvexity properties are proposed for set-valued maps, which are natural generalizations of the g-diagonal quasiconvexity for real functions. Together with an application of continuous selection and fixed-point theorems, these conditions enable us to prove unified existence results of solutions for the system of generalized vector quasi-variational-like inequalities. The results of this paper can be seen as extensions and generalizations of several known results in the literature.

ALGORITHM OF SOLUTIONS FOR MIXEDNONLINEAR VARIATIONAL-LIKE INEQUALITIES IN REFLEXIVE BANACH SPACE

In this paper, the author studies a class of mixed nonlinear variational-like inequalities in reflexive Banach space. By applying a minimax inequality obtained by the author, some existence uniqueness theorems of solutions for the mixed nonlinear variational-like inequalities are proved. Next, by applying the auxiliary problem technique, rite author suggests an innovative iterative algorithm to compute the approximate solutions of the mixed nonlinear variational-like inequalities. Finally, the convergence criteria is also discussed.

THE EXISTENCE AND UNIQUENESS OF SOLUTIONS OF GENERALIZED VARIATIONAL INEQUALITIES ARISING FROM ELASTICITY WITH FRICTION

The existence and uniqueness of solutions of generalized variational inequalities arising from elasticity with friction, which is equivalent to corresponding elemental problems, is elucidated in detail, and then FEM approximation and discrete methods are proposed.

GENERALIZED VARIATIONAL PRINCIPLE ON NONLINEAR THEORY OF NATURALLY CURVED AND TWISTED CLOSED THIN-WALLED COMPOSITE BEAMS

Naturally curved and twisted closed thin-walled slender beams of composite material undergoing small strains, large displacements and rotations have been investigated, and an incomplete generalized variational function on theory of elasticity with finite displacement is established far these beams with complete constrained boundaries at two ends. The balance equations as well as all boundary conditions concerned have been deduced from functional stationary value condition. The above-mentioned method can also be extended to other various incomplete constrained boundaries conveniently. In addition, the fundamental equations and concerned formulas in the small displacement theory of the beams can be derived by using above results.

Lyapunov Inequalities of Nonlinear Discrete Systems

In this paper, we study the nonlinear discrete systems and obtain several lyapunov inequalities for them. Then we give the application for lyapunov inequality.

A General Projection Method for a System of Relaxed Coercive Variational Inequalities in Hilbert Spaces

In this paper,we consider a new algorithm for a generalized system for relaxed coercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods.Our results include the previous results as special cases extend and improve the main results obtained by many others.

EXISTENCE AND ITERATIVE ALGORITHMS OF SOLUTIONS FOR GENERALIZED MIXED QUASI_VARIATIONAL INEQUALITIES

In this paper, by using the auxiliary technique of variational inequalities, the existence and iterative algorithm; of solutions for a class of generalized mixed quasi-variational inequalities are studied. Our results answer the open problems mentioned by Noor, improve and generalize some recent known results.

ON ITERATIVE ALGORITHMS FOR A CLASS OF NONLINEAR VARIATIONAL INEQUALITIES

In this paper we use the auxiliary principle technique to suggest and analyze novel and innovative iterative algorithms for a class of nonlinear variational inequalities. Several special cases, which can be obtained from our main results, are also discussed.

EXISTENCE OF SOLUTIONS FOR GENERALIZEDQUASI-VARIATIONAL-LIKE INEQUALITIES

In this paper, some existence theorems of solutions for a class of generalized quasi-variational-like inequalities with discontinuous mappings ape proved under paracompact setting in topological vector spaces. These theorems unify, improve and generalize many recent results.

THE APPLICATIONS OF GENERALIZED VARIATIONAL PRINCIPLES IN NONLINEAR STRUCTURAL ANALYSIS

This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form of namely, the physical equations of structures have the shape of exponential functions. Several examples are given to illustrate the statically indeterminate structures such as the trusses, beams, frames and torsional bars.

A system of general nonlinear variational inclusions in Banach spaces

A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.

Existence and Algorithm of Solutions for Generalized Mixed Implicit Quasi-Variational-Like Inequalities

By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.

Existence of Solutions to Generalized Vector Quasi-variational-like Inequalities with Set-valued Mappings

In this paper, we introduce and study a class of generalized vector quasivariational-like inequality problems, which includes generalized nonlinear vector variational inequality problems, generalized vector variational inequality problems and generalized vector variational-like inequality problems as special cases. We use the maximal element theorem with an escaping sequence to prove the existence results of a solution for generalized vector quasi-variational-like inequalities without any monotonicity conditions in the setting of locally convex topological vector space.

A PROJECTION-TYPE ALGORITHM FOR SOLVING GENERALIZED MIXED VARIATIONAL INEQUALITIES

We propose a projection-type algorithm for generalized mixed variational in- equality problem in Euclidean space Rn. We establish the convergence theorem for the pro- posed algorithm, provided the multi-valued mapping is continuous and f-pseudomonotone with nonempty compact convex values on dom（f）, where f ： Rn --RU{＋∞} is a proper func- tion. The algorithm presented in this paper generalize and improve some known algorithms in literatures. Preliminary computational experience is also reported.

A FRACTIONAL NONLINEAR EVOLUTIONARY DELAY SYSTEM DRIVEN BY A HEMI-VARIATIONAL INEQUALITY IN BANACH SPACES

This article deals with a new fractional nonlinear delay evolution system driven by a hemi-variational inequality in a Banach space.Utilizing the KKM theorem,a result concerned with the upper semicontinuity and measurability of the solution set of a hemivariational inequality is established.By using a fixed point theorem for a condensing setvalued map,the nonemptiness and compactness of the set of mild solutions are also obtained for such a system under mild conditions.Finally,an example is presented to illustrate our main results.

OPTIMAL CONTROL OF PARABOLIC VARIATIONAL INEQUALITIES WITH STATE CONSTRAINT

The optimal control problem of parabolic variational inequalities with the state constraint and nonlinear, discontinuous nonmonotone multivalued mapping term and its approximating problem are studied, which generalizes some obtained results.

Asymptotic Behavior of Global Solution for Nonlinear Generalized Euler-Possion-Darboux Equation

J. L Lions and W. A. Stranss [1] have proved the existence of a global solution of the initial boundary value problem for nonlinear generalized Euler-Possion-Darboux equation. In this paper we are going to investigate the asymptotic behavior of the global solution by a difference inequality.