EXISTENCE AND NONEXISTENCE FOR THE INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEM OF MULTIDIMENSIONAL NONLINEAR SCHRDINGER EQUATIONS WITH OPERATOR AND THEIR SOLITON SOLUTIONS

The nonlinear interactions between the monochromatic wave have been considered by K. Matsunchi, who also proposed one class of the nonlinear Schrdinger equation system with wave operator. We also obtain the same type of equations, which are satisfied by transverse velocity of higher frequency electron, as we study soliton in plasma physics. In this paper, under some condition we study the existence and nonexistence for this equations in the cases possessing different signs in nonlinear term.

ON THE EXISTENCE AND NODAL CHARACTER OF SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

In this paper we prove the existence of k-node solution of singular nonlinear boundary value problems for each k is-an-element-of N union {0}.

ON THE EXISTENCE AND NODAL CHARACTER OF THE SOLUTIONS OF SINGULAR NONLINEAR BOUNDARY VALUE PROBLEMS

1. Introduction We consider the singular nonlinear boundary value problem where l=v+3/v-1,l+1 is the critical exponent of the embedding of weighted Sobolev space Wt21,2（O, +∞） into Lt2q（O, ∞）, v>2. When v=N-1 we can get the radial solutions of problem where 2*=2N/N-2 is the critical exponent of the Sobolev embedding H1（Rn）→LQ（RN）. Kurtz has discussed the existence of κ-node solution of （1.1）, （1.2） for each κ∈N U{0} when the growth rate of |u|l-1u+f（u） is lower then |u|v+3/v-1 i.e.

AN APPLICATION OF SCHAUDER’S FIXED POINT THEOREM TO THE EXISTENCE OF SOLUTlONS OF IMPULSIVELY DIFFERENTIAL EQUATIONS

In this paper the existence of solutions of a boundary value problem forimpulsively differential equations that is difficult to solve by the upper and lowersolution method will be proved by means of Schauder’s fixed point theorem,whichimproves some existing results.

THE INITIAL BOUNDARY VALUE PROBLEM FOR QUASI-LINEAR SCHRODINGER-POISSON EQUATIONS

In this article, the author studies the iuitial （Dirichlet.） boundary problem for a high field version of the Schroedinger-Poisson equations, which include a nonlinear term in the Poisson equation corresponding to a field-dependent dielectric constant and an effective potential in the Schroedinger equations on the unit cube. h global existence and uniqueness is established for a solution to this problem.

Application of complex nonlinear modes to determine dry whip motion in a rubbing rotor system

Dry whip motion is an instability of rubbing rotor system and may cause catastrophic failures of rotating machinery.Up to now,the related mechanisms of the dry whip is still not well understood.This paper aims to build the relationship between the complex nonlinear modes and the dry whip motion,and propose an effective method to predict the response characteristics and existence boundary of the dry whip through complex nonlinear modes.For the first time,the paper discusses how to use the complex nonlinear modes to predict the dry whip systematically,and as a consequence,the mechanism of the relationship between the complex nonlinear mode and the dry whip is revealed.The results show that the Backward Whirl(BW)mode motion of the rubbing rotor system dominates the response characteristics and the existence boundary of dry whip.The whirl amplitude and whirl frequency of dry whip are equal to the modal amplitude and modal frequency of the BW mode at the jump up point where the modal damping is equal to zero.The existence boundary corresponds to the critical rotation speed where the minimum of the modal damping of the BW mode motion is exactly equal to zero.Moreover,the proposed nonlinear modal method in this article is very effective for the prediction of dry whip of the more complicated practical rotor system,which has been verified by applying the predicted method into a rubbing rotor test rig.

On Systems of Boundary Value Problems for Differential Inclusions

Herein we consider the existence of solutions to second-order, two-point boundary value problems （BVPs） for systems of ordinary differential inclusions. Some new Bernstein-Nagumo conditions are presented that ensure a priori bounds on the derivative of solutions to the differential inclusion. These a priori bound results are then applied, in conjunction with appropriate topological methods, to prove some new existence theorems for solutions to systems of BVPs for differential inclusions. The new conditions allow of the treatment of systems of BVPs without growth restrictions.