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1

Analytic functions in the unit ball of bounded L-index in joint variables and of bounded L-index in direction: a connection between these classes

Bandura Andriy, Skaskiv Oleh

Demonstratio Mathematica

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2019

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Vol. 52, nr 1

82--87

EN

We give negative answer to the question of Bordulyak and Sheremeta for more general classes of entire functions than in the original formulation: Does index boundedness in joint variables for an entire function F imply index boundedness in the variable zj for the function F? This question is addressed for entire functions of bounded L-index in joint variables and entire functions of bounded L-index in direction. We also present a class of analytic functions in the unit ball which has bounded L-index in joint variablesand has unbounded l-index in the variables z1 and z2 for any positive continuous function l : B2→C.

2

The existence of a unique solution of the hyperbolic functional differential equation

Karpowicz A.

Demonstratio Mathematica

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2014

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Vol. 47, nr 4

866--877

EN

We consider the Z. Szmydt problem for the hyperbolic functional differential equation. We prove a theorem on existence of a unique classical solution and the Carathéodory solution of the hyperbolic equation.

3

Existence results for second-order impulsive neutral functional differential inclusions in Banach spaces

Bahaj M., Cherti I.

Journal of Applied Analysis

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2012

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Vol. 18, nr 2

225-242

EN

In this paper, we investigate the existence of mild solutions on a compact interval to second-order impulsive neutral functional differential inclusions in Banach spaces. The results are obtained by using the theory of continuous cosine families and a fixed point theorem due to Dhage.

4

Upper and lower solutions method for fourth-order periodic boundary value problems

Weng S., Gao H., Jiang D., Hou X.

Journal of Applied Analysis

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2008

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Vol. 14, nr 1

53-61

EN

The purpose of this paper is to prove the existence of a solution of the following periodic boundary value problem {u(4)(t) = ∫(t, u(t), u" (t), t ∈ [0, 2π] {u(0) = u(2π]), u' (0) = u' (2π), u" (0) = u' (2π), u''' (2π) in the presence of an upper solution β ≤ α, where ∫(t, u, v) satisfies one side Lipschitz condition.

5

Positive solutions for a class of nonresonant m-point boundary value problems

Feng M., Zhang X., Ge W.

Journal of Applied Analysis

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2008

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Vol. 14, nr 1

115-129

EN

This paper concerns the existence and multiplicite of positive solutions for a class of nonresonant m-point boundary-value problem of second-order diferential equations Lx = λw(t)(t, x), 0ρ -integrable for some 1≤ p ≤ +∞. the arguments are based upen fixed point theorems in a cone and Hoelder's inequqlity. The nonexistence of positive solution is also studied. In addistion, some examples are included to demonstrate the main results.

6

The existence theory for the differential equation xm(t)=f(t,x) in Banach spaces and Henstock-Kurzweil integral

Sikorska-Nowak A.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

115-124

EN

Using the properties of the Henstock–Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x(m)(t) = f(t, x) in a Banach space, where f is HL integrable and satis.es certain conditions. Our fundamental tool is the measure of noncompactness developed by Kuratowski and Hausdorff.