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.

The Solutions for Adjustment and Reconstruction of Water-Drive Surface Systems in the Old Areas of Daqing Oilfield

Introduction Owing to long-time running, more facilities including stations, pipelines, vessels have become corrosive and aged ,some process has grown old, it has exert more burden for the maintenance and repair.Simultaneously, the fluid production rate, oil production rate and water injection rate has changed greatly so that the inflicts and problems from the established surface systems will become more obvious. Energy cost of production and running has increasing continuously. Capacity has been unbalance in systems and areas.

Uniqueness of the Viscosity Solutions for the Initial Value Problem of One Type of Second Order Partial Differential Equation

Aim To prove the uniqueness of the viscosity solutions for the initial value problems of one type of second order parabolic partial differential equations: Methods Using comparison theorem. Results and Conclusion If u0 is uniform continuousfunction in RN , F is continuous function in RNx(N) and F is degenerate elliptic, then thisequation has the sole viscosity solution.

ON THE SOLUTIONS OF NAVIER-STOKES EQUATIONS AND THE THEORY OF HOMOGENEOUS ISOTROPIC TURBULENCE

The present paper is a further development of our previous work in solving the wholeproblem of the homogeneous isotropic turbulence from the nitial period to the final period ofdecay. An expansion method is developed to obtain the axinlly symmetrical solution of theNavier-Stokes equations of motion in the form of an infinite set of nonlinear partial differen-tial equations of the second order. For the present we solve the zeroth order approximation.By using the method of Fourier transform, we get a nonlinear nitegro-differential equationfor the amplitude function in the wave number space.It is also the dynamical equation forthe energy spectrum. By choosing a suitable initial condition, we solve this equation numerically. The energyspectrum function and the energy transfer spectrum function thus calculated satisfy the spec-trum form of the karman-Howarth equation exactly. We Lave computed the energy spectrumfunction, the energy transfer function the decay of turbulent energy, the integral scale, Taylormicroscale, the double and triple velocity correlations on the whole range from the initialperiod to the final period of decay. As a whole all these calculated statistical physicalquantities agree with experiments very wall except a few cases with small discrepancies at largeseparations.

ESTIMATES ON THE SOLUTIONS OF CERTAIN HIGHER ORDER FINITE DIFFERENCE EQUATIONS

In this paper results on the estimates for solutions of certain higher order finite difference equations are established. The main tool employed in our analysis is based on the applications of the discrete inequality which provides an explicit bound on the unknown function.

On the Propagation of the Analytic Regularity in Strictly Hyperbolic Equations Which Are Lipschitz Continuous With Respect to Time

We consider strictly hyperbolic nonlinear equations which are Lipschitz continuous in the time variable and study the local analytic regularity of the solutions with respect to the space variables.