On conjugacy of high-order linear ordinary differential equations.
On conjugate points of solutions of non-selfadjoint differential systems
On connecting orbits of semilinear parabolic equations on .
On critical points for noncoercive functionals and subharmonic solutions of some Hamiltonian systems.
On differential equations in normal form.
On distance between zeros of solutions of third order differential equations
The lower bounds of the spacings b-a or a’-a of two consecutive zeros or three consecutive zeros of solutions of third order differential equations of the form y”’ + q(t)y’ + p(t)y = 0 (*) are derived under very general assumptions on p and q. These results are then used to show that or as n → ∞ under suitable assumptions on p and q, where ⟨tₙ⟩ is a sequence of zeros of an oscillatory solution of (*). The Opial-type inequalities are used to derive lower bounds of the spacings d-a or b-d for...
On distribution of zeros of solutions of the differential equation
On equation on the line
On equation of finite type, 1-special, with the same central dispersion of the first kind
On Existence and Asymptotic Properties of Kneser Solutions to Singular Second Order ODE.
We investigate an asymptotic behaviour of damped non-oscillatory solutions of the initial value problem with a time singularity , , on the unbounded domain . Function is locally Lipschitz continuous on and has at least three zeros , and . The initial value . Function is continuous on has a positive continuous derivative on and . Asymptotic formulas for damped non-oscillatory solutions and their first derivatives are derived under some additional assumptions. Further, we provide...
On existence of Kneser solutions of a certain class of -th order nonlinear differential equations
The paper deals with existence of Kneser solutions of -th order nonlinear differential equations with quasi-derivatives.
On existence of nonoscillatory solutions in forced nonlinear differential equations.
On existence of oscillatory solution of the system of differential equations
On Existence of Positive Periodic Solutions.
On existence of proper solutions of quasilinear second order differential equations.
On existence of singular solutions of -th order differential equations
On families of trajectories of an analytic gradient vector field
For an analytic function f:ℝⁿ,0 → ℝ,0 having a critical point at the origin, we describe the topological properties of the partition of the family of trajectories of the gradient equation ẋ = ∇f(x) attracted by the origin, given by characteristic exponents and asymptotic critical values.
On first integrals for polynomial differential equations on the line
We show that any equation dy/dx = P(x,y) with P a polynomial has a global (on ℝ²) smooth first integral nonconstant on any open domain. We also present an example of an equation without an analytic primitive first integral.
On first-order differential operators with Bohr-Neugebauer type property.
On focal points and limit behavior of solutions of linear differential equations