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1.
New oscillation and nonoscillation criteria are established for the equation
,where p :]1,+[ R is the locally integrable function. These criteria generalize and complement the well known criteria of E. Hille, Z. Nehari, A. Wintner, and P. Hartman. 相似文献
2.
A. Lomtatidze 《Georgian Mathematical Journal》1995,2(1):93-98
The sufficient conditions are established under which the second-order linear differential equation is conjugate. 相似文献
3.
4.
We establish efficient conditions guaranteeing that every solution of the problem
u¢(t) 3 l(u)(t), u(a) 3 h(u), u'(t) \geq \ell (u)(t),\quad u(a) \geq h(u), 相似文献
5.
Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established. 相似文献
6.
For higher order ordinary differential equations, new sufficient conditions on the existence and uniqueness of periodic solutions
are established. Results obtained cover the case when the right-hand side of the equation is not of a constant sign with respect
to an independent variable. 相似文献
7.
The problem on the existence of a positive in the interval ]a, b[ solution of the boundary value problem
is considered, where the functions f and
satisfy the local Carathéodory conditions. The possibility for the functions f and g to have singularities in the first argument (for t = a and t = b) and in the phase variable (for u = 0) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established. 相似文献
8.
We establish unimprovable sufficient conditions for the unique solvability of the boundary-value problem
9.
We study the question of the existence, uniqueness, and continuous dependence on parameters of the Carathéodory solutions to the Cauchy problem for linear partial functional-differential equations of hyperbolic type. A theorem on the Fredholm alternative is also proved. The results obtained are new even in the case of equations without argument deviations, because we do not suppose absolute continuity of the function the Cauchy problem is prescribed on, which is rather usual assumption in the existing literature. 相似文献
10.
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