Plato’s recollection argument in the "Philebus" [PDF]
Many scholars have denied that Plato’s argument about desire at Philebus 34c10–35d7 is related to his recollection arguments in the Meno and Phaedo, because it is concerned only with postnatal experiences of pleasure.
Iwata, Naoya
core +1 more source
A representation theorem for the linear quasi‐differential equation (py′)′+qy=0
We establish a representation for q in the second‐order linear quasi‐differential equation (py′)′+qy=0. We give a number of applications, including a simple proof of Sturm′s comparison theorem.
J. G. O′Hara
wiley +1 more source
On an isolation and a generalization of Hölder′s inequality
We generalize the well‐known Hölder inequality and give a condition at which the equality holds.
Xiaojing Yang
wiley +1 more source
A sturm separation theorem for a linear 2n th order self‐adjoint differential equation
For the 2nth order equation, (−1) nv(2n) + qv = 0, with q continuous, we obtain a Sturm Separation theorem, involving n + 1 solutions of the equation, which is somewhat analogous to the classical result that the zeros of two linearly independent solutions of the second order equation separate each other.
Charles T. Fulton +2 more
wiley +1 more source
Interval Criteria for Forced Oscillation of Functional Differential Equations with γ-Laplacian, Damping and Mixed Nonlinearities [PDF]
2010 Mathematics Subject Classification: 34C10 ...
Elabbasy, E. M. +3 more
core +1 more source
Existence of asymptotic solutions of second order neutral differential equation with multiple delays
The existence of positive solutions of second order neutral differential equation of the form is investigated. Some sufficient conditions are given for the existence of positive solutions with asymptotic decay of (A). Examples are presented to illustrate the results.
S. C. Palaniswami
wiley +1 more source
Positive solutions of integrodifferential equations
Integrodifferential equations of the forms are considered, where K ∈ C([0, ∞), [0, ∞)), p ∈ C([0, ∞), [0, ∞)) and q ∈ C((−∞, ∞), [0, ∞)). Necessary conditions and also sufficient conditions for the existence of positive solutions are established.
Ch. G. Philos
wiley +1 more source
Oscillation and non‐oscillation of some neutral differential equations of odd order
An existence criterion for nonoscillatory solution for an odd order neutral differential equation is provided. Some sufficient conditions are also given for the oscillation of solutions of some nth order equations with nonlinearity in the neutral term.
B. S. Lalli, B. G. Zhang
wiley +1 more source
Oscillation criteria in neutral equations of n order with variable coefficients
Consider the n‐order neutral delay differential equation where P,Q ∈ C[[t0, ∞), ℝ] and the delays τ and σ are nonnegative real numbers. In this paper we examined the oscillatory behavior of the solutions of the above equation using techniques which allow the relaxation of the restrictions which has been introduced previously.
D. A. Georgiou, C. Qian
wiley +1 more source
Existence of positive solutions for neutral differential equations
We establish sufficient conditions for the existence of positive solutions of the neutral delay differential equation .
Q. Chuanxi, G. Ladas
wiley +1 more source

