一类自共轭非线性差分方程的振动性

Oscillation of a Self-Conjugate Nonlinear Difference Equation

自共轭差分方程的振动性的研究已经引起了人们的广泛关注,对于高阶自共轭差分方程的振动性已经有了最新成果,而非线性不稳定型差分方程的振动性还未发现有效的结论.通过讨论最终正解和最终负解的不存在性,来研究高阶自共轭非线性不稳定型差分方程振动的判断准则.

Tha research of oscillation of the serf- conjugate nonlinear differenco equation has already aroused people＇s interest, and oscillation of the higher order has had the latest achievement, but there is not an effective conclusion of the oscillation of non - nonlinear unstable type. Through the discussion of the nonexistence of the final positive and negative solution, we have obtained the criterion of higher order self- conjugate non - linearity unstable difference equation.