Existence and non-existence of maximal solutions for y" = f(x, y, y') *
Existence and non-existence of sign-changing solutions for a class of two-point boundary value problems involving one-dimensional -Laplacian
We consider the boundary value problem involving the one dimensional -Laplacian, and establish the precise intervals of the parameter for the existence and non-existence of solutions with prescribed numbers of zeros. Our argument is based on the shooting method together with the qualitative theory for half-linear differential equations.
Existence of asymptotic solutions of second order neutral differential equation with multiple delays.
Existence of conjugate points for second-order linear differential equations.
Existence of oscillatory and nonoscillatory solutions for a class of neutral functional differential equations
For a certain class of functional differential equations with perturbations conditions are given such that there exist solutions which converge to solutions of the equations without perturbation.
Existence of oscillatory solutions for functional differential equations of neutral type.
Existence of positive solutions to vector boundary value problems. II.
Factoring linear differential operators on measure chains.
First phases of the associated equation with parameters for the differential equation
Fixed point analysis for non-oscillatory solutions of quasi linear ordinary differential equations
The paper deals with the quasi-linear ordinary differential equation with . We treat the case when is not necessarily monotone in its second argument and assume usual conditions on and . We find necessary and sufficient conditions for the existence of unbounded non-oscillatory solutions. By means of a fixed point technique we investigate their growth, proving the coexistence of solutions with different asymptotic behaviors. The results generalize previous ones due to Elbert–Kusano, [Acta...
Forced oscillation of second order nonlinear dynamic equations on time scales.
Forced oscillation of second-order half-linear dynamic equations on time scales.
Forced oscillation of second-order nonlinear dynamic equations on time scales.
Forced oscillation of third order nonlinear dynamic equations on time scales
Consider the third order nonlinear dynamic equation , (*) on a time scale which is unbounded above. The function f ∈ C(,) is assumed to satisfy xf(x) > 0 for x ≠ 0 and be nondecreasing. We study the oscillatory behaviour of solutions of (*). As an application, we find that the nonlinear difference equation , where α ≥ -1, γ > 0, c > 3, is oscillatory.
Forced oscillations of first order nonlinear neutral differential equations.
Forced superlinear oscillations via Picone's identity.
Friedrichs extension of operators defined by linear Hamiltonian systems on unbounded interval
In this paper we consider a linear operator on an unbounded interval associated with a matrix linear Hamiltonian system. We characterize its Friedrichs extension in terms of the recessive system of solutions at infinity. This generalizes a similar result obtained by Marletta and Zettl for linear operators defined by even order Sturm-Liouville differential equations.
From the recollections of Otakar Borůvka -- the founder of the Brno school of differential equations
Fundamental central dispersion in a simple system
Fundamental central dispersions in a double system