Li and Shaked (2007) introduced the family of generalized total time on test transform (TTT) stochastic orders, which is parameterized by a real function h that can be used to capture the preferences of a decision maker. It is natural to look for properties of these orders when there is an uncertainty in determining the appropriate function h. In this paper we study these orders when h is nonde...

This paper investigates global asymptotic stability (GAS) and global exponential stability (GES) of a class of continuous-time recurrent neural networks. First, we introduce a necessary and sufficient condition for existence and uniqueness of equilibrium of the neural networks with Lipschitz continuous activation functions. Next, we present two sufficient conditions to ascertain the GAS of the ...

We study the existence of weak solutions to (E) (−∆)u+g(u) = ν in a bounded regular domain Ω in R (N ≥ 2) which vanish in R \Ω, where (−∆) denotes the fractional Laplacian with α ∈ (0, 1), ν is a Radon measure and g is a nondecreasing function satisfying some extra hypotheses. When g satisfies a subcritical integrability condition, we prove the existence and uniqueness of a weak solution for pr...

We show that the reaction-diffusion system ut = ∆φ(u) + f (v), vt = ∆ψ(v) + g(u), with homogeneous Neumann boundary conditions, has a positive global solution on Ω× [0,∞) if and only if ∫∞ds/ f (F−1(G(s)))=∞ (or, equivalently, ∫∞ds/g(G−1(F(s)))=∞), where F(s) = ∫ s 0 f (r)dr and G(s) = ∫ s 0 g(r)dr. The domain Ω ⊆ RN (N ≥ 1) is bounded with smooth boundary. The functions φ, ψ, f , and g are non...

We present some sufficient conditions such that Eq. (1) only has solutions with zero points in (0,∞). Moreover, we also obtain some conditions such that Eq. (1) has a positive solution on [0,+∞). The motivation of this work comes from the work of Ladas, Philos and Sficas [5]. They discussed the oscillation behavior of Eq. (1) when P (t, s) = P (t− s) and g(t) = t. They obtained a necessary and ...

We study the limit behaviour of solutions of ∂tu−∆u+h(|x|) |u| p−1 u = 0 in R × (0, T ) with initial data kδ0 when k → ∞, where h is a positive nondecreasing function and p > 1. If h(r) = r, β > N(p−1)−2, we prove that the limit function u∞ is an explicit very singular solution, while such a solution does not exist if β ≤ N(p−1)−2. If lim infr→0 r 2 ln(1/h(r)) > 0, u∞ has a persistent singulari...

In this paper we pose some important queuing problems, make some conjectures about their solution, and present some evidence in support of the conjectures. We consider the standard GI/G/s queueing model with s homogeneous servers in parallel, unlimited waiting room, the first-come first-served discipline and lid (independent and identically distributed) service times (with a general distributio...

We study the existence of positive solution for the system  −∆u = λa(x)[f(v)− 1 uα ], x ∈ Ω −∆v = λb(x)[g(v)− 1 vβ ], x ∈ Ω u = v = 0, x ∈ ∂Ω, where λ is a positive parameter, Ω is a bounded domain with smooth boundary, α, β ∈ (0, 1). Here a(x) and b(x) are C sing-changing functions that maybe negative near the boundary and f , g are C nondecreasing functions, such that f, g : (0,∞) → (0,∞); ...