Cm SOLUTIONS OF SYSTEMS OF FINITE DIFFERENCE EQUATIONS
نویسندگان
چکیده
Let R be the real number axis. Suppose that G, H are Cm maps from R2n+3 to R. In this note, we discuss the system of finite difference equations G(x,f (x), f (x+1), . . . ,f (x+n),g(x),g(x+1), . . . ,g(x+n))= 0 and H(x,g(x),g(x+1), . . . , g(x+n),f (x),f (x+1), . . . ,f (x+n)) = 0 for all x ∈ R, and give some relatively weak conditions for the above system of equations to have unique Cm solutions (m≥ 0).
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