Results 11 to 20 of about 73 (73)
On certain comparison theorems for half‐linear dynamic equations on time scales
Abstract and Applied Analysis, Volume 2004, Issue 7, Page 551-565, 2004., 2004 We obtain comparison theorems for the second‐order half‐linear dynamic equation [r(t)Φ(yΔ)]Δ+p(t)Φ(yσ)=0, where Φ(x) = |x|α−1sgn x with α > 1. In particular, it is shown that the nonoscillation of the previous dynamic equation is preserved if we multiply the coefficient p(t) by a suitable function q(t) and lower the exponent α in the nonlinearity Φ ...
Pavel Řehák
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On the discreteness of the spectra of the Dirichlet and Neumann p‐biharmonic problems
Abstract and Applied Analysis, Volume 2004, Issue 9, Page 777-792, 2004., 2004 We are interested in a nonlinear boundary value problem for (|u″|p−2u″)′′=λ|u|p−2u in [0, 1], p > 1, with Dirichlet and Neumann boundary conditions. We prove that eigenvalues of the Dirichlet problem are positive, simple, and isolated, and form an increasing unbounded sequence. An eigenfunction, corresponding to the nth eigenvalue, has precisely n − 1
Jiří Benedikt
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Oscillation for advanced differential equations with oscillating coefficients
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 33, Page 2109-2118, 2003., 2003 Some sufficient conditions are established for the oscillation of all solutions of the advanced differential equation x′(t) − p(t)x(t + τ) = 0, t ≥ t0, where the coefficient p(t) ∈ C([t0, ∞), R) is oscillatory, and τ is a positive constant.
Xianyi Li, Deming Zhu, Hanqing Wang
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A representation theorem for the linear quasi‐differential equation (py′)′+qy=0
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 8, Page 579-584, 2000., 2000 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
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On an isolation and a generalization of Hölder′s inequality
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 1, Page 59-61, 2000., 2000 We generalize the well‐known Hölder inequality and give a condition at which the equality holds.
Xiaojing Yang
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A sturm separation theorem for a linear 2n th order self‐adjoint differential equation
International Journal of Stochastic Analysis, Volume 8, Issue 1, Page 29-46, 1995., 1994 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
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Existence of asymptotic solutions of second order neutral differential equation with multiple delays
International Journal of Stochastic Analysis, Volume 8, Issue 1, Page 77-83, 1995., 1994 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
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Positive solutions of integrodifferential equations
International Journal of Stochastic Analysis, Volume 6, Issue 1, Page 55-68, 1993., 1992 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
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Oscillation and non‐oscillation of some neutral differential equations of odd order
International Journal of Mathematics and Mathematical Sciences, Volume 15, Issue 3, Page 509-515, 1992., 1991 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
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Oscillation criteria in neutral equations of n order with variable coefficients
International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 4, Page 689-696, 1991., 1991 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
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