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• W1984577887 abstract "The linear autonomous system of difference equations x(n+1)=Ax(n) is considered, where [email protected]?R^k,A is a real nonsingular kxk matrix. In this paper it has been proved that if W(x) is any homogeneous polynomial of m-th degree in x, then there exists a unique homogeneous polynomial V(x) of m-th degree such that @DV=V(Ax)-V(x)=W(x) if and only if @l1^i^^1,@l2^i^^2,...,@lk^i^^k 1(i1+i2+...+ik=m,ij>=0) where @l1,@l2,...,@lk are the eigenvalues of the matrix A. The theorem on the instability has also been proved." @default.
• W1984577887 created "2016-06-24" @default.
• W1984577887 creator A5086914601 @default.
• W1984577887 date "2010-03-01" @default.
• W1984577887 modified "2023-09-26" @default.
• W1984577887 title "Homogeneous polynomials as Lyapunov functions in the stability research of solutions of difference equations" @default.
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• W1984577887 doi "https://doi.org/10.1016/j.amc.2010.01.026" @default.
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