On the existence of solutions for equations with accretive mappings in probabilistic normed spaces

The purpose of this paper is to introduce the concept of accretive mapping inprobabilistic normed space(PN space,in short)and to study the existence problem ofsolutions for equations with accretive mappings in PN space and some existence theoremsare shown.     

Fixed Points of Multi-valued Maps and Static Coulomb Friction Problems

The existence of solutions to the Signorini problem with Coulomb friction is a long standing open question. We prove the existence of generalized solutions that satisfy the pointwise Coulomb friction conditions on the entire interface and the normal nonpenetration condition on the complement of a subset with arbitrarily small but possibly positive measure. Furthermore, the penetration itself can also be made arbitrarily small. Although “measure zero” instead of “arbitrarily small measure” would be needed to fully resolve the issue, these generalized solutions seem to be the closest answer available to date. Their existence is proved by a suitable application of Ky Fan's fixed point theorem for multi-valued maps. The same method can be used with a number of variants involving contact of two or more elastic bodies and possible debonding phenomena. This revised version was published online in August 2006 with corrections to the Cover Date.     

Existence and Approximation of Solutions to Variational Inclusions with Accretive Mappings in Banach Spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅｓｕｐｐｏｓｅｔｈａｔＸｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ,Ｘ ｉｓｉｔｓｄｕａｌｓｐａｃｅ ,〈· ,·〉ｉｓｔｈｅｐａｉｒｉｎｇｏｆＸａｎｄＸ .Ｄ(Ｔ)ａｎｄＲ(Ｔ)ｄｅｎｏｔｅｔｈｅｄｏｍａｉｎａｎｄｔｈｅｒａｎｇｅｏｆＴｒｅｓｐｅｃｔｉｖｅｌｙ .ＬｅｔＴ ,Ａ :Ｘ →Ｘ ,ｇ :Ｘ→Ｘ ｂｅｔｈｒｅｅｍａｐｐｉｎｇｓａｎｄφ :Ｘ →Ｒ∪ ∞ ａｐｒｏｐｅｒｃｏｎｖｅｘｌｏｗｅｒｓｅｍｉ＿ｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎ .Ｉｎ 1 999,ｔｈ…     

Schubart Solutions in the Charged Collinear Three-Body Problem

In this paper, we study the existence of Schubart-like periodic solutions in a charged collinear three-body problem by applying the notion of turning points and some continuity arguments. We proved the existence of Schubart solutions for the case where the outer particles repel each other.     

On the Problem of Dissipative Perturbations of Nonexpansive Mappings

ＩｎｔｒｏｄｕｃｔｉｏｎａｎｄＰｒｅｌｉｍｉｎａｒｉｅｓＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ｗｅａｓｓｕｍｅｔｈａｔＨｉｓａｒｅａｌＨｉｌｂｅｒｔｓｐａｃｅ ,〈· ,·〉ｉｓｔｈｅｉｎｎｅｒｐｒｏｄｕｃｔｏｎＨ ,ＰｉｓａｃｏｎｅｉｎＨ .ＢｙｖｉｒｔｕｅｏｆｔｈｅｃｏｍｅＰ ,ａｎｏｒｄｅｒ“≤”ｉｓｉｎｄｕｃｅｄｉｎＨ ,ｉ.ｅ .,ｆｏｒａｎｙｇｉｖｅｎｘ,ｙ∈Ｈ ,ｘ≤ｙｉｆａｎｄｏｎｌｙｉｆｙ -ｘ∈Ｐ .Ａｍｕｌｔｉ＿ｖａｌｕｅｄｍａｐｐｉｎｇＡ :Ｄ(Ａ) Ｈ → 2 Ｈｉｓｓａｉｄｔｏｂｅａｃｃｒｅｔｉｖ…     

Existence of bounded solutions on the real line for Liénard system

The existence of monotone and non-monotone solutions of boundary value problem on the real line for Liénard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Liénard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.     

On the periodic solutions of differential inclusions and applications

The periodic problem of evolution inclusion is studied and its results are used toestablish existence theorems of periodic solutions of a class of semi-linear differential inclusion.Also existence theorem of the extreme solutions and the strong relaxation theorem are given forthis class of semi-linear differential inclusion. An application to some feedback control systems isdiscussed.     

Generalized Strongly Nonlinear Quasi-Complementarity Problems

ＧＥＮＥＲＡＬＩＺＥＤＳＴＲＯＮＧＬＹＮＯＮＬＩＮＥＡＲＱＵＡＳＩ－ＣＯＭＰＬＥＭＥＮＴＡＲＩＴＹＰＲＯＢＬＥＭＳＬｉＨｏｎｇ－ｍｅｉ（李红梅）ＤｉｎｇＸｉｅ－ｐｉｎｇ（丁协平）（ＳｉｃｈｕａｎＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ），Ｃｈｅｎｇｄｕ（Ｒｅ...     

Self-similar singular solution of fast diffusion equation with gradient absorption terms

The self-similar singular solution of the fast diffusion equation with nonlinear gradient absorption terms are studied. By a self-similar transformation, the self-similar solutions satisfy a boundary value problem of nonlinear ordinary differential equation (ODE). Using the shooting arguments, the existence and uniqueness of the solution to the initial data problem of the nonlinear ODE are investigated, and the solutions are classified by the region of the initial data. The necessary and sufficient condition for the existence and uniqueness of self-similar very singular solutions is obtained by investigation of the classification of the solutions. In case of existence, the self-similar singular solution is very singular solution.     

Autonomous noetherian boundary-value problem in the critical case

We establish constructive conditions for the existence of solutions of an autonomous Noetherian weakly nonlinear boundary-value problem for a system of ordinary differential equations in the critical case and develop a modified iterative procedure for finding its solutions.     

Generalized complementarity problems for fuzzy mappings

In this paper we introduce a new class of generalized complementarity problems for the fuzzy mappings and construct a new iterative algorithm. We also discuss the existence of solutions for the generalized complementarity problems and the convergence of tterative sequence.     

Unbounded Branches of Classical Injective Solutions to the Forced Displacement Problem in Nonlinear Elastostatics

We consider classical solutions of the equilibrium equations of nonlinear elastostatics under prescribed boundary displacements and body forces, both of which depend on a loading parameter. We employ recent results on global continuation [HS] that establish general existence of global continua of solutions in nonlinear elastostatics. Under reasonable hypotheses on the stored energy function we prove the existence of an unbounded branch of globally injective solutions to the boundary value problem. This revised version was published online in August 2006 with corrections to the Cover Date.     

Elxed Point Theorem of Composition g-Contraction Mapping and its Applications

ＩｎｔｒｏｄｕｃｔｉｏｎＭａｎｙｓｔｕｄｉｅｓｈａｖｅｂｅｅｎｄｏｎｅｏｎｃｏｎｔｒａｃｔｉｖｅｍａｐｐｉｎｇｓ,ｅ .ｇ .,Ｒｈｏａｄｅｓ[1]ｍａｄｅａｃｏｍｐａｒｉｓｏｎｏｆｖａｒｉｏｕｓｄｅｆｉｎｉｔｉｏｎｓ (ｍｏｒｅｔｈａｎ 1 0 0ｔｙｐｅｓｖａｒｉｅｄｆｒｏｍ 2 5ｂａｓｉｃｔｙｐｅｓ)ｏｆｃｏｎｔｒａｃｔｉｖｅｍａｐｐｉｎｇｏｎｃｏｍｐｌｅｔｅｍｅｔｒｉｃｓｐａｃｅｉｎ 1 977.Ａｎｄｕｐｔｏｎｏｗ ,ｓｕｃｈｓｔｕｄｙｉｓｓｔｉｌｌｇｏｉｎｇｏｎ ,ｅ .ｇ .,[2 ] .Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｓｅ…     

On the Investigation of One Semiexplicit System of Differential Equations in the Case of a Variable Pencil of Matrices

We investigate a semiexplicit Cauchy problem for a system of ordinary differential equations in the case of a variable pencil of matrices. We determine sufficient conditions of existence of solutions and consider the problem of their number.     

A new approach for the solution of singular optimum in structural topology optimization

In order to overcome the difficulties caused by singular optima, in the present paper, a new method for the solutions of structural topology optimization problems is proposed. The distinctive feature of this method is that instead of solving the original optimization problem directly, we turn to seeking the solutions of a sequence of approximated problems which are formulated by relaxing the constraints of the original problem to some extent. The approximated problem can be solved efficiently by employing the algorithms developed for sizing optimization problems because its solution is not singular. It can also be proved that when the relaxation parameter is tending to zero, the solution of the approximated problem will converge to the solution of the original problem uniformly. Numerical examples illustrate the effectiveness and validity of the present approach. Results are also compared with those obtained by traditional methods. The project supported by the National Natural Science Foundation of China under project No. 19572023     

EXISTENCE OF BOUNDED SOLUTIONS ON THE REAL LINE FOR LIENARD SYSTEM

The existence of monotone and non-monotone solutions of boundary value problem on the real line for Lienard equation is studied. Applying the theory of planar dynamical systems and the comparison method of vector fields defined by Lienard system and the system given by symmetric transformation or quasi-symmetric transformation, the invariant regions of the system are constructed. The existence of connecting orbits can be proved. A lot of sufficient conditions to guarantee the existence of solutions of the boundary value problem are obtained. Especially, when the source function is bi-stable, the existence of infinitely many monotone solusion is obtained.     

Study of a new semi-continuous model of the Boltzmann equation

For a semi-continuous model of the Boltzmann equation (1) peculiar solutions are obtained and generally the global existence of solutions of the initial value problem is discussed. The global existence is possible even in some cases for partially negative initial number densities, which are not physical problems, but mathematical ones. It can be shown that in some cases the entropy begins to increase, reaches a maximum and decreases again.     

A non-linear eigenvalue problem: The shape at equilibrium of a confined plasma

A free boundary value problem arising in plasma physics is reduced to a non-linear eigenvalue problem of a non-classical type. We establish the existence of solutions of the non-linear eigenvalue problem; these solutions are critical points of appropriate functionals.     

MULTI-VALUED QUASI VARLATIONAL INCLUSIONS IN BANACH SPACES

The purpose is to introduce and study a class of more general multivalued quasi variational inclusions in Banach spaces.By using the resolvent operator technique some existence theorem of solutions and iterative approximation for solving this kind of multivalued quasi variational inclusions are established.The results generalize,improve and unify a number of Noor's and others' recent results.     

SOME FURTHER GENERALIZATIONS OF KY FAN’S MINIMAX INEQUALITY AND ITS APPLICATIONS TO VARIATIONAL INEQUALITIES

The purpose of this paper is to introduce the concept of generalized KKM mapping andto obtain some general version of the famous KKM theorem and Ky Fan’s minimaxinequality.As applications,we utilize the results presented in this paper to study the saddlepoint problem and the existence problem of solutions for a class of quasi-variationalinequalities.The results obtained in this paper extend and improve some recent results of[1-6].