Alexander Lomtatidze

On a two-point boundary value problem for the second order ordinary differential equations with singularities

V clanku jsou nalezeny postacujici podminky pro řesitelnost dvoubodove okrajove ulohy pro singularni obycejne diferencialni rovnice druheho řadu.

On periodic solutions of first order linear functional differential equations

New optimal sufficient conditions are established for the existence of a unique periodic solution of first order scalar functional differential equations

On oscillation and nonoscillation of a second-order half-linear equation.

Abstract New oscillation and nonoscillation criteria are established for the equation u″ + p(t)|u| α |u′|1–α sgn u = 0, where α ∈]0, 1] and the function p :]0, +∞[→] – ∞, +∞[ is locally integrable.

On a periodic-type boundary value problem for first-order nonlinear functional differential equations

Nonimprovable,in a certain sense, sufficient conditions for the unique solvability of antiperiodic type BVP for first order scalar functional differential equations are established.

On the Periodic Boundary Value Problem for First-Order Functional-Differential Equations

V clanku jsou nalezeny efektivni podminky zarucujici řesitelnost periodicke ulohy pro funkcionalni diferencialni rovnice prvniho řadu.

Oscillation and Nonoscillation Criteria for Two-Dimensional Systems of First Order Linear Ordinary Differential Equations

Sufficient conditions are established for the oscillation and nonoscillation of the system

Periodic Problem Involving Quasilinear Differential Operator and Weak Singularity

Abstract We study the singular periodic boundary value problem of the form (|u′|p−2 u′)′ = f(t, u), u(0) = u(T), u′(0) = u′(T), where 1 < p < ∞ and f ∈ Car([0, T] × (0,∞)) can have a repulsive space singularity at x = 0. Contrary to previous results by Mawhin and Jebelean, Liu Bing and Rachůnková and Tvrdý, we need not assume any strong force conditions. Our main existence results rely on a new antimaximum principle for periodic quasilinear periodic problem, which has an independent meaning.

ON NONNEGATIVE SOLUTIONS OF A CERTAIN BOUNDARY VALUE PROBLEM FOR FIRST ORDER LINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS

Unimprovable efficient conditions are established for the existence and uniqueness of a nonnegative solution of the problem u′(t) = `(u)(t) + q(t), u(a) = h(u) + c, where ` : C([a, b]; R) → L([a, b]; R) is a linear bounded operator, h : C([a, b]; R) → R is a linear bounded functional, q ∈ L([a, b]; R) and c > 0.

SOLVABILITY AND THE UNIQUE SOLVABILITY OF A PERIODIC TYPE BOUNDARY VALUE PROBLEM FOR FIRST ORDER SCALAR FUNCTIONAL DIFFERENTIAL EQUATIONS

Abstract Nonimprovable in a certain sense, sufficient conditions for the solvability and unique solvability of the problem 𝑢′ (𝑡) = 𝐹 (𝑢) (𝑡), 𝑢(𝑎) – λ𝑢(𝑏) = ℎ(𝑢) are established, where 𝐹 : 𝐶([𝑎, 𝑏]; 𝑅) → 𝐿([𝑎, 𝑏];𝑅) is a continuous operator satisfying the Carathéodory condition, ℎ : 𝐶([𝑎, 𝑏]; 𝑅) → 𝑅 is a continuous functional, and λ ∈ 𝑅+.

Linear Hyperbolic Functional-Differential Equations with Essentially Bounded Right-Hand Side

Theorems on the unique solvability and nonnegativity of solutions to the characteristic initial value problem 𝑢(1,1)(𝑡,𝑥)=l0(𝑢)(𝑡,𝑥)