Abstract: The study of linear and global.properties of linear dynamical systems on vector bundles appeared rather extensive already in the past.Presently we propose to study perturbations of this linear dynamics The perturbed dynamical system which we shallconsider is no longer linear.while the properties to be studied will be still global in general.Moreover.we are interested in the nonuniformly hyperbolic properties.In this paper,we set an appropriate definition for such perturbations.Though it appears somewhat not quite usual yet has deeper root in standard systens of differential equations in the theory of differentiable dynamical systens The general problen is to see which property of the original given by the dynamical system is persistent when a perturbation takes place.The whole contenl of the paper is deyoted to establishing a theorem of this sort.
Abstract: In this paper,a class of new KKM theorem is obtained which unifies and improves the correspontiling results in [2,3,6,7,11].As applications.we utilize our resultto obtain some matching theorem,coincidence theorem,coincidence theorem.fixed point theorem,mini-max inequality theorem and section theorem.
Abstract: The traditional semi-inverse solution method of the Saint tenant problem.whichis described in foe Euclidian space under the Lagrange syslemformulation,is updated to be solved in the symplectic space under foe conservative Hamiltonian system.It isproved in the present paper that all the Saint Venant solutions can be obtained directlyvia the zero eigenvalue solutions and all their Jordan normal form of the corresponding Hamiltonian operator matrix.
Abstract: By using coordinate and nearly,identical transformations.the strongly nonlinear Duffing system is reduced to normal form in this paper.and then the bifurcation equations with different resonant conditions and their solutions are obtained.The local bifurcation diagrams and the transition sets on unfolding parmeter and physical parameter plane are analysized by singularity theory.
Abstract: In this paper.by using a minimax inequality obtained by the author,some existence theorems of Pareto equilibria for multicriteria games without compactness,continuity and concavity are proved in toplogical vector spaces and reflexive Banach spaces.
Abstract: This is an expand of the complex function method in solving the problem of interaction of plane.SH-waves and non-circular cavity surfaced with linig in anisotropic media.the use the method similar to that incorporated in  added with Savin's method for solving stress concentration of non-circular cavity surfaced with lining in elasticity.Anisotropic media can be used ic simulate the conditions of thegeology.The solving proceeding for this problem can be processed conveniently in the manner similar to that introduced in .In this paper.as illustrated in example numerical studies have been done for a square cavity surfaced with lining in anisotropic media.
Abstract: A shortout analytic method of stability in Strong non-linear autonomous system is introduced into stability analysis of the themohaline double-diffusive system.Using perturbation technique obtains conditions of existence and stability for linear and nonlinear periodic solutions.For linear periodic solution in infinitesimeal motion the existence range of monotomic branch and oscillatory branch are outilined.The oscillatory branch of nonlinear periodic solution in finite-amplitude motion has unstable periodic solution when μ is smaller than critical value μc in this case of 0s-rsc<<1.The stability conclusions under different direction of vortex are drawn out .
Abstract: In this paper,for viscous incompressible Navier-Stokes equations with periodic bonndary conditions,we prove the existence and uniqueness ot the solution corresponding to its Fourier nonlinear Galerkin approximation.At the same time we give its error estimates.
Abstract: In this paper we study the forced oscillations of boundary value problems of a class of higher order functional partial differential equations.The principal tool is an everaging techniqe which enables one to establish oscillation in terms of related functional differential inequalities.