In the paper we employ the notion of weighted sharing of sets to deal with the well known question of Gross and obtain a uniqueness result on meromorphic functions sharing two sets which will improve an earlier result of Lahiri [14] .

The existence of ground state solutions for the quasi-linear elliptic equation

$$-\mbox{div}(|\nabla u|^{p-2}\nabla u)=\rho(x)f(u),\;\;\mbox {in}\;\;{\bf R^N}$$

under suitable conditions is proved. We modify the method developed in [Z. Yang, Existence of positive entire solutions for singular and non-singular quasi-linear elliptic equation, J. Comput. Appl. Math. 197 (2006) 355-364] and extend the results of [A.Mohammed, Ground state solutions for singular semi-linear elliptic equations, Nonlinear Analysis(in press) and Teodora-Liliana Dinu, Entire solutions of sublinear elliptic equations in anisotropic media, J. Math. Anal. Appl. 322(2006), 382-392.]

The main goal of this paper is to show that the concept of generalized differentiability introduced by the authors in [2] allows to obtain new solutions to the fuzzy differential equations. A very general existence and uniqueness result of two solutions for the fuzzy differential equations with modified argument and based on generalized differentiability is obtained together with a characterization of these solutions by ODEs. Real-world applications consisting in applications to fuzzy pantograph equation that models the cell growth and to fuzzy logistic equation that models the population dynamics under uncertainty are presented. In particular, as collateral consequences we correct some results on generalized differentiability recently obtained by Y. Chalco-Cano and H. Román-Flores in [7]and propagated in a characterization result obtained by J.J. Nieto, A. Khastan and K. Ivaz in [21].

This paper concerns the unicity of entire functions and the growth estimate of entire solutions to certain complex linear non-homogenous differential equations.

Let $k$ be a natural number and $s$ be real. In the 1-dimensional case, the $k$-th order derivatives of the functions $\lvert x\rvert^s$ and $\log \lvert x\rvert$ are multiples of $\lvert x\rvert^{s-k}$ and $\lvert x\rvert^{-k}$, respectively. In the present paper, we generalize this fact to higher dimensions by introducing a suitable norm of the derivatives, and give the exact values of the multiples.

In this paper we consider a wave equation with a weak frictional damping. We establish an explicit and general decay rate result, using some properties of convex functions. Our result is obtained without imposing any restrictive growth assumption on the frictional damping term..

This paper aims at initial-boundary value problems(IBVP) for the isothermal compressible Euler equations with damping on bounded domains. We first prove global existence and uniqueness of classical solutions for smooth initial data. Time asymptotically, it is shown that the density converges to its average over the domain and the momentum vanishes as time tends to infinity. Due to diffusion and boundary effects, the convergence rate is shown to be exponential. Second, based on the entropy principle, it is shown that similar results hold for $L^\infty$ entropy weak solutions.

Reiterated deterministic homogenization problem for nonlinear pseudo monotone parabolic type operators is considered beyond the usual periodic setting. We present a new approach based on the generalized Besicovitch type spaces, which allows to consider general assumptions on the coefficients of the operators under consideration. In particular we solve the weakly almost periodic homogenization problem and many new other problems such as the homogenization in the Fourier-Stieltjes algebra. Our approach falls within the scope of multiscale convergence method.

We treat in this paper the problem of stability of a class of parameter dependent perturbed systems. Furthermore, the problem of stabilization using an estimated state feedback is developed. Under some sufficient conditions, we construct, first, an observer which provides an estimation of the state, then we consider the system in closed loop by the state estimated feedback. The results of this paper are illustrated by numerical examples..

In this paper, we investigate existence for a class of partial neutral functional integrodifferential equations with infinite delay. Using the integrated semigroup theory and the well known Banach fixed point theorem, we establish local existence and uniqueness of integral solutions to these equations. To illustrate our abstract results, we conclude this work by an example. .