On the oscillation of solutions of self-adjoint linear differential equations of the fourth order
On the oscillation of solutions of self-adjoint linear differential equations of the fourth order
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四阶自伴线性微分方程解的振荡
DOI：
10.1090/s0002-9947-1958-0102639-x
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发表时间：
1958
期刊：
影响因子：
--
通讯作者：
Z. Nehari
中科院分区：
文献类型：
--
作者：
W. Leighton;Z. Nehari
其中，在所考虑的区间中，r(X)、q(X)和P(X)分别是C“、C和C的函数，素数表示关于x的微分。除非有明确的相反声明，否则将假设所有这些函数都是在区间(0，00)中定义的，并且属于所指示的类别。简单的例子表明，一般方程(1.1)包括具有完全不同的振荡行为的方程。因此，为了更深入地研究(1.1)的解，有必要引入反映这些基本差异的某些方程子类(1.1)之间的区别。从类似的二阶方程中得到提示
where, in the interval considered, r(x), q(x) and P(x) are functions of C", C and C, respectively, and the prime denotes differentiation with respect to x. Unless there is an explicit statement to the contrary, it will be assumed that all these functions are defined, and belong to the classes indicated, in the interval (0, oo). Simple examples show that the general equation (1.1) includes equations of radically different oscillatory behavior. For a more penetrating study of the solutions of (1.1) it is therefore necessary to introduce distinctions between certain sub-classes of equations (1.1) which reflect these basic differences. Taking our cue from the analogous second-order equation