Linear perturbations of general disconjugate equations
Linearisation of second-order differential equations.
Given a second order differential equation on a manifold we find necessary and sufficient conditions for the existence of a coordinate system in which the system is linear. The main tool to be used is a linear connection defined by the system of differential equations.
Linearization and higher order nonlinear oscillation theorems using comparison methods.
Linearized comparison criteria for a nonlinear neutral differential equation
A class of nonlinear neutral differential equations with variable coefficients and delays is considered. Conditions for the existence of eventually positive solutions are obtained which extend some of the criteria existing in the literature. In particular, a linearized comparison theorem is obtained which establishes a connection between our nonlinear equations and a class of linear neutral equations with constant coefficients.
Lineárne homogénne diferenciálne rovnice druhého rádu rýdzo diskonjugované vzhľadom na derivácie
Logarithmic derivatives of solutions of disconjugate differential equations
Lp-Perturbations of Second Order Linear Differential Equations.
Lyapunov type inequalities for a second order differential equation with a damping term
For a second order differential equation with a damping term, we establish some new inequalities of Lyapunov type. These inequalities give implicit lower bounds on the distance between zeros of a nontrivial solution and also lower bounds for the spacing between zeros of a solution and/or its derivative. We also obtain a lower bound for the first eigenvalue of a boundary value problem. The main results are proved by applying the Hölder inequality and some generalizations of Opial and Wirtinger type...
Lyapunov type integral inequalities for certain differential equations.
Lyapunov-type inequality for higher-order differential equations
Maximal regularity of the discrete harmonic oscillator equation.
Methods of oscillation theory of half-linear second order differential equations
In this paper we investigate oscillatory properties of the second order half-linear equation Using the Riccati technique, the variational method and the reciprocity principle we establish new oscillation and nonoscillation criteria for (*). We also offer alternative methods of proofs of some recent oscillation results.
Minimal and maximal solutions of fourth order iterated differential equations with singular nonlinearity
In this paper we are concerned with sufficient conditions for the existence of minimal and maximal solutions of differential equations of the form where is the iterated linear differential operator of order and is a continuous function.
Monotone and Oscillatory Solutions of a Class of Nonlinear Differential Equations
Monotonic properties of zeros and extremants of the differential equation
Monotonicity properties of oscillatory solutions of differential equation
We obtain monotonicity results concerning the oscillatory solutions of the differential equation . The obtained results generalize the results given by the first author in [1] (1976). We also give some results concerning a special case of the above differential equation.
Monotonicity properties of the linear combination of derivatives of some special functions
Monotonicity theorems concerning differential equations
More on oscillation of th-order equations.
Multiple solutions of a third order boundary value problem