Abstract:
This paper deals with a class of nonlinear elliptic equations inan unbounded domain D of ℝn, n≥3, with a nonempty compact boundary, where the nonlinear term satisfies someappropriate conditions related to a certain Kato classK∞(D). Our purpose is to give some existence results andasymptotic behaviour for positive solutions by using the Greenfunction approach and the Schauder fixed point theorem.

Abstract:
This paper deals with a class of nonlinear elliptic equations in an unbounded domain D of n , n≥3 , with a nonempty compact boundary, where the nonlinear term satisfies some appropriate conditions related to a certain Kato class K ∞ ( D ) . Our purpose is to give some existence results and asymptotic behaviour for positive solutions by using the Green function approach and the Schauder fixed point theorem.

Abstract:
We study the existence and the asymptotic behaviour of positive solutions for the nonlinear singular elliptic equation $Delta u +varphi(.,u)=0$ in the outside of the unit disk in $mathbb{R}^2$, with homogeneous Dirichlet boundary condition. The aim is to prove some existence results for the above equation in a general setting by using a potential theory approach.

Abstract:
We prove some existence of positive solutions to the semilinear elliptic system $$displaylines{ Delta u =lambda p(x)g(v)cr Delta v =mu q(x)f(u) }$$ in the half space ${mathbb{R}}^n_+$, $ngeq 2$, subject to some Dirichlet conditions, where $lambda$ and $mu$ are nonnegative parameters. The functions $f, g$ are nonnegative continuous monotone on $(0,infty)$ and the potentials $p, q$ are nonnegative and satisfy some hypotheses related to the Kato class $K^infty({mathbb{R}}^n_+)$.

Abstract:
Let $D$ be an unbounded domain in $mathbb{R}^{n}$ ($ngeq 2$) with a nonempty compact boundary $partial D$. We consider the following nonlinear elliptic problem, in the sense of distributions, $$displaylines{ Delta u=f(.,u),quad u>0quad hbox{in }D,cr uig|_{partial D}=alpha varphi ,cr lim_{|x|o +infty }frac{u(x)}{h(x)}=eta lambda , }$$ where $alpha ,eta,lambda $ are nonnegative constants with $alpha +eta >0$ and $varphi $ is a nontrivial nonnegative continuous function on $partial D$. The function $f$ is nonnegative and satisfies some appropriate conditions related to a Kato class of functions, and $h$ is a fixed harmonic function in $D$, continuous on $overline{D}$. Our aim is to prove the existence of positive continuous solutions bounded below by a harmonic function. For this aim we use the Schauder fixed-point argument and a potential theory approach.

Abstract:
This article concerns radially symmetric positive solutions of second-order quasilinear elliptic systems. In terms of the growth of the variable potential functions, we establish conditions such that the solutions are either bounded or blow up at infinity.

Abstract:
We study some existence results for the nonlinear equation (1/A)(Au')'=uψ(x,u) for x∈(0,ω) with different boundary conditions, where ω∈(0,∞], A is a continuous function on [0,ω), positive and differentiable on (0,ω), and ψ is a nonnegative function on (0,ω)×[0,∞) such that t↦tψ(x,t) is continuous on [0,∞) for each x∈(0,ω). We give asymptotic behavior for positive solutions using a potential theory approach.

Abstract:
We prove the existence of a solution, decaying to zero at infinity, for the second order differential equation $$ frac{1}{A(t)}(A(t)u'(t))'+phi(t)+f(t,u(t))=0,quad tin (a,infty). $$ Then we give a simple proof, under some sufficient conditions which unify and generalize most of those given in the bibliography, for the existence of a positive solution for the semilinear second order elliptic equation $$ Delta u+varphi(x,u)+g( |x|) x. abla u =0, $$ in an exterior domain of the Euclidean space ${mathbb{R}}^{n},ngeq 3$.

Abstract:
Target tracking using wireless sensor networks offers multiple challenges because it usually involves
intensive computation and requires accurate methods for tracking and energy consumption.
Above all, scalability, energy optimization, efficiency, and overhead reduction are some
among the key tasks for any protocol designed to perform target tracking using large scale sensor
networks. Border surveillance systems, on the other side, need to report border crossings in a real
time manner. They should provide large coverage, lower energy consumption, real time crossing
detection, and use efficient tools to report crossing information. In this paper, we present a
scheme, called Border Cooperative and Predictive Tracking protocol (BCTP), capable of energyaware
surveillance and continuous tracking of objects and individuals’ crossing a country border
and anticipating target motion within a thick strip along the border and estimating the target exit
zone and time.