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the equation
In particular, we find a finite dimensional matrix B, constructed from the coefficientscα of the equation (I-B)q=p, where the vectorp depends on h.
      
By the equation, the dichromatic sum function can be found explicitly.
      
The existence of infinitely many solutions for the equation are given by means of variational method, where ∞,if n = 1,2.
      
The existence of positive radial solutions of the equation-div(|Du|p-2Du)=f(u) is studied in annular domains in Rn, n≥2.
      
If f(0)>amp;lt;0 and satisfies certain conditions, then the equation has no radial solution if the annuli are too wide.
      
Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.
      
The existence of a traveling wave solution to the above piece-wise linear equation has been proved by solving the equation explitly (McKenna >amp;amp; Walter in 1990).
      
The existence and uniqueness of classical global solutions and the nonexistence of global solutions to the first boundary value problem and the second boundary value problem for the equation utt-a1uxx-a2uxxt=?(ux)x are proved.
      
Assume that the coefficient functions a(x), β(x) and γ(x) are asymptotically periodic and satisfy 1 A positive homoclinic orbit of the equation is obtained by means of variational methods.
      
The coefficient k in the equation is found to be a critical parameter.
      
The equation discussed in this paper and the methods used here are extension and complement to the corresponding results of Wei Li and He Zhen's previous papers.
      
Under the weak Lipschitz condition about the solution of the equation, convergence theorems for a family of iterations with one parameter are obtained.
      
This paper also suggests sufficient and necessary conditions for the existence and uniqueness of solutions and explicit forms of the solutions of the equation.
      
The equation discussed and the methods shown in the paper are continuation and complement to the corresponding results of Li and Zhen's previous papers.
      
Correlations were highly significant (P>amp;lt;0.001) for foliage biomass, branch biomass and total biomass, among which the equation of the total biomass was the highest.
      
In addition, the continuous dependence of the solution of this equation on the linear dispersive coefficient contained in the equation is obtained.
      
In the equation, differential viscosity and the first normal stress function are defined to specify the rheological properties of non-Newtonian medium.
      
Then, by analyzing the vibration of the piezoelectric vibrator, the vibration deformation function and the equation of volume change are established.
      
Heavy-ion reactions induced by neutron-rich nuclei provide a unique means to investigate the equation of state of isospin-asymmetric nuclear matter, especially the density dependence of the nuclear symmetry energy.
      
In this paper, the equation of state of the ternary system 15%LiF-58%NaF-27%BeF2, over the temperature range from 873.15 to 1 073.15 K at one atmosphere pressure, is described using a modified Peng-Robinson (PR) equation.
      
 

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