Volume 25 (2017), Issue 2

1. Existence of solutions for a coupled system with ∅-Laplacian operators and nonlinear coupled boundary conditions

Konan Charles Etienne Goli ; Assohoun Adjé.
We study the existence of solutions of the system submitted to nonlinear coupled boundary conditions on [0, T] where ∅1, ∅2: (-a, a) → ℝ, with 0 < a < +∞, are two increasing homeomorphisms such that ∅1(0) = ∅2(0) = 0, and fi : [0, T] × ℝ4 → ℝ, i ∈{1, 2} are two L1-Carathéodory functions. Using some new conditions and Schauder fixed point Theorem, we obtain solvability result.

2. Oscillation and Periodicity of a Second Order Impulsive Delay Differential Equation with a Piecewise Constant Argument

Gizem S. Oztepe ; Fatma Karakoc ; Huseyin Bereketoglu.
This paper concerns with the existence of the solutions of a second order impulsive delay differential equation with a piecewise constant argument. Moreover, oscillation, nonoscillation and periodicity of the solutions are investigated.

3. Isometries of Riemannian and sub-Riemannian structures on three-dimensional Lie groups

Rory Biggs.
We investigate the isometry groups of the left-invariant Riemannian and sub-Riemannian structures on simply connected three-dimensional Lie groups. More specifically, we determine the isometry group for each normalized structure and hence characterize for exactly which structures (and groups) the isotropy subgroup of the identity is contained in the group of automorphisms of the Lie group. It turns out (in both the Riemannian and sub-Riemannian cases) that for most structures any isometry is the composition of a left translation and a Lie group automorphism.

4. Convolution of second order linear recursive sequences II.

Tamás Szakács.
We continue the investigation of convolutions of second order linear recursive sequences (see the first part in [1]). In this paper, we focus on the case when the characteristic polynomials of the sequences have common root.

5. Estimating the critical determinants of a class of three-dimensional star bodies

Werner Georg Nowak.
In the problem of (simultaneous) Diophantine approximation in ℝ3 (in the spirit of Hurwitz’s theorem), lower bounds for the critical determinant of the special three-dimensional body K2 : (y2 + z2)(x2 + y2 + z2) ≤ 1 play an important role; see [1], [6]. This article deals with estimates from below for the critical determinant ∆ (Kc) of more general star bodies Kc : (y2 + z2)c/2(x2 + y2 + z2) ≤ 1 ; where c is any positive constant. These are obtained by inscribing into Kc either a double cone, or an ellipsoid, or a double paraboloid, depending on the size of c.

6. The Existence of a Generalized Solution of an m-Point Nonlocal Boundary Value Problem

David Devadze.
An m-point nonlocal boundary value problem is posed for quasi- linear differential equations of first order on the plane. Nonlocal boundary value problems are investigated using the algorithm of reducing nonlocal boundary value problems to a sequence of Riemann-Hilbert problems for a generalized analytic function. The conditions for the existence and uniqueness of a generalized solution in the space are considered.