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
On forced periodic oscillations in dissipative Liénard systems
On functional integrability of solutions of differential equations with deviating argument
On functions describing a distribution of zeros of solutions of an iterated linear differential equation of the fourth order
On generalized periodic solutions of linear differential equations of order n
On geometric detection of periodic solutions and chaotic dynamics.
On global transformations of functional-differential equations of the first order
The paper describes the general form of functional-differential equations of the first order with delays which allows nontrivial global transformations consisting of a change of the independent variable and of a nonvanishing factor. A functional equation for is solved on and a method of proof by J. Aczél is applied.
On global transformations of ordinary differential equations of the second order
The paper describes the general form of an ordinary differential equation of the second order which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form is solved on for ,
On gradient at infinity of semialgebraic functions
Let f: ℝⁿ → ℝ be a C² semialgebraic function and let c be an asymptotic critical value of f. We prove that there exists a smallest rational number such that |x|·|∇f| and are separated at infinity. If c is a regular value and , then f is a locally trivial fibration over c, and the trivialisation is realised by the flow of the gradient field of f.
On Halphen and Laguerre-Forsyth canonical forms of linear differential equations
On holomorphic foliations without algebraic solutions.