一类中立型拟线性抛物方程组解的振动性

一类中立型拟线性抛物方程组解的振动性 Oscillations of Solutions to a Class of Systems of Quasilinear Parabolic Equations of Neutral Type 刘霞文 LIU Xia-wen~ 1 2 3 4 first-author 刘伟安 1 2 3 4 武汉大学数学与统计学院 武汉大学数学与统计学院 1,2),LIU Wei-an~1 1,2),LIU Wei-an~1 武汉大学数学与统计学院,湖北,武汉,430072 武汉大学数学与统计学院,湖北,武汉,430072 株洲工学院信息与计算科学系 株洲工学院信息与计算科学系 ,湖南,株洲,412008 ,湖南,株洲,412008 针对垂直相加法无法讨论泛函偏微分方程组的强迫振动性的不足,直接利用振动的定义、Green公式以及齐次Neumann边界条件把中立型抛物微分方程组的振动问题转化为泛函微分不等式不存在最终正解的问题,然后利用最终正解的定义及上下极限得到了在齐次Neumann边界条件下判别其所有解振动或全振动的充分条件. Aim at the shortage of vertically additive method by which we can’t discuss forced oscillations of systems of partial functional differential equations,we directly use the oscillatory definition,Green’s formula and boundary condition of homogeneous Neumann to change the oscillatory problem of solutions to a class of systems of quasilinear parabolic equations of neutral type into the problem of which functional differential inequality haven’t eventually positive solution.And we use the definition of（eventually） positive solution,limit superior and limit inferior to obtain sufficient conditions for oscillation or full oscillation of their solutions subject to boundary condition of homogeneous Neumann type. 中立型 拟线性 抛物微分方程 方程组 振动 neutral type quasilinear parabolic differential equation systems oscillation O175.26 2005-05-01 2021-04-01 5