Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2012
Volume
Vol. 32
Number
No. 1
Description
Journal Volume
Opuscula Mathematica
Vol. 32 (2012)
Projects
Pages
Articles
Fixed points and stability in neutral nonlinear differential equations with variable delays
(2012) Ardjouni, Abdelouaheb; Djoudi, Ahcene
By means of Krasnoselskii’s fixed point theorem we obtain boundedness and stability results of a neutral nonlinear differential equation with variable delays. A stability theorem with a necessary and sufficient condition is given. The results obtained here extend and improve the work of C.H. Jin and J.W. Luo [Nonlinear Anal. 68 (2008), 3307–3315], and also those of T.A. Burton [Fixed Point Theory 4 (2003), 15-32; Dynam. Systems Appl. 11 (2002), 499–519] and B. Zhang [Nonlinear Anal. 63 (2005), e233–e242]. In the end we provide an example to illustrate our claim.
Compactly supported multi-wavelets
(2012) Banaś, Wojciech
In this paper we show some construction of compactly supported multi-wavelets In $L^2(\mathbb{R}^d)$, $d \geq 2$ which is based on the one-dimensional case, when $d = 1$. We also demonstrate that some methods, which are useful in the construction of wavelets with a compact support at $d = 1$, can be adapted to higher-dimensional cases if $A \in M_{d \times d}(\mathbb{Z})$ is an expansive matrix of a special form.
Weak solutions for nonlinear fractional differential equations with integral boundary conditions in Banach spaces
(2012) Benchohra, Mouffak; Mostefai, Fatima-Zohra
The aim of this paper is to investigate a class of boundary value problems for fractional differential equations involving nonlinear integral conditions. The main tool used in our considerations is the technique associated with measures of weak noncompactness.
Isospectral integrability analysis of dynamical systems on discrete manifolds
(2012) Blackmore, Denis L.; Prykarpatski, Anatolij; Prikarpats'kìj, Ârema A.
It is shown how functional-analytic gradient-holonomic structures can be used for an isospectral integrability analysis of nonlinear dynamical systems on discrete manifolds. The approach developed is applied to obtain detailed proofs of the integrability of the discrete nonlinear Schrödinger, Ragnisco-Tu and Riemann-Burgers dynamical systems.
Note on the stability of first order linear differential equations
(2012) Bojor, Florin
In this paper, we will prove the generalized Hyers-Ulam stability of the linear differential equation of the form $y'(x)+f(x)y(x)+g(x)=0$ under some additional conditions.