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- A. Lomtatidze
- 2001

Sufficient conditions for oscillation and nonoscillation of second-order linear equations are established. 1. Statement of the Problem and Formulation of Basic Results Consider the differential… (More)

- A. Lomtatidze, N. PARTSVANIA
- 2002

Sufficient conditions are established for the oscillation and nonoscillation of the system u′ = p(t)v , v′ = −q(t)u , where p, q : [0, +∞[→ [0, +∞[ are locally summable functions. § 1. Statement of… (More)

- A. Lomtatidze, ZDENĚK OPLUŠTIL

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];… (More)

We investigate oscillatory properties of the second order half-linear differential equation ðrðtÞFðy 0ÞÞ 0 þ cðtÞFðyÞ 1⁄4 0; FðsÞ :1⁄4 jsj s; p > 1; ð*Þ viewed as a perturbation of a nonoscillatory… (More)

- Alberto Cabada, A. Lomtatidze, Milan Tvrdý
- 2007

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 p ∈ (1,∞) and f ∈ Car([0, T ] × (0,∞) can have a repulsive space… (More)

- A. Lomtatidze, S. Mukhigulashvili, J. Sremr
- Mathematical and Computer Modelling
- 2008

On the rectangleD = [a, b]×[c, d], the problem on the existence and uniqueness of a nonnegative solution of the characteristic initial value problem for the equation ∂2u(t, x) ∂t ∂x = `(u)(t, x)+… (More)

- A. Lomtatidze, J. Sremr
- 2009

The aim of the paper is to find efficient conditions for the unique solvability of the problem u′(t) = `(u)(t) + q(t), u(a) = h(u) + c, where ` : C([a, b];R) → L([a, b];R) and h : C([a, b];R) → R are… (More)

- Alexander Domoshnitsky, A. Lomtatidze, Abraham Maghakyan, Jiřı́ Šremr
- 2014

and Applied Analysis 3 vii L∞ D;R is the Banach space of Lebesgue measurable and essentially bounded functions p : D → R equipped with the norm ∥p∥L∞ ess sup {∣∣p t, x ∣∣ : t, x ∈ D}. 2.2 viii L∞ D;R… (More)

On the rectangle D = [a, b]× [c, d], the problem on the existence and uniqueness of a nonnegative solution of the characteristic initial value problem for the equation ∂u(t, x) ∂t ∂x = `(u)(t, x) +… (More)

- A. Lomtatidze
- 2001

Sufficient conditions for the solvability of two-point boundary value problems for the system xi = fi(t, x1, x2) (i = 1, 2) are given, where f1 and f2 : [a1, a2]×R → R are continuous functions. 1.… (More)

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