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In this paper we study the Goursat problem for semilinear hyperbolic equations with zero boundary condition where the boundary is the characteristic cone for hyperbolic operator.
      
Based on the literature [1], this paper changes the essential conditionα ∫g(t)/tr(s)ds ≤ 1 into∫g(t)/tr(s)ds ≤θ.
      
In this paper we will give a new inversion formula and a simple necessary and sufficient condition which guarantees the complete reconstruction algorithm.
      
The equivalent condition of this optimal design is given.
      
The exact soliton solutions are given and the relation between this condition and the known results in the literature is also discussed.
      
A locally semicomplete digraph is a digraph D = (V,A) satisfying the following condition: for every vertex x ∈ V the D[O(x)] and D[I(x)] are semicomplete digraphs.
      
In this paper the characterization of admissible condition in terms of the Fourier transform is given.
      
In this paper, a necessary condition for a bipartite graph λKm,n to be K1.k-factorizable and a sufficient condition for kKm,n to have a K1,k-factorization whenever k is a prime number are given.
      
This result coincides with the classical one under condition r'=r.
      
The existence of such an equilibrium is proved under the following condition: continuous, weakly convex, strictly monotone and complete preferences, strictly positive endowments and dividends processes.
      
The condition that the double points of the curve must satisfy is given.
      
A necessary and sufficient condition for singular nonlinear second-order boundary value problems to have positive solutions
      
In this paper, a sufficient condition for boundedness and persistence of the solutions of the following delay difference equation is obtained.
      
We establish the convergence theories of this class of generalized parallel multisplitting relaxation methods under the condition that the system matrix is an H-matrix with positive diagonal elements.
      
This paper deals with the steady state bifurcation of the K-S equation in two spatial dimensions with periodic boundary value condition and of zero mean.
      
This paper deals with the blow-up properties of solutions to semilinear heat equation with the nonlinear boundary condition .
      
Different from rational quadratic Bézier curves, the value is generally related with the location of the ray, and the necessary and sufficient condition of the ratio being independent of the ray's location is showed.
      
The new optimality condition doesn't use Luderer's regularity assumption and its Lagrangian multipliers don't depend on the particular elements in the superdifferentials of the object function and constraint functions.
      
At the same time, a necessary and sufficient condition for the equality of the spectrum of Q(G) and L(G) is given.
      
In this note it is shown that a necessary and sufficient condition for the existence of a P3-factorization of complete multipartite graph λKmn is (1) m≥3, (2) mn≡0 (mod 3) and (3) λ(m-1)n≡0(mod 4).
      
 

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