We study the asymptotic behavior of solutions to the second-order evolution equation p(t)u ′′ (t) + r(t)u ′ (t) ∈ Au(t) a.e. t ∈ (0,+∞), u(0) = u0, sup t≥0|u(t)| < +∞, where A is a maximal monotone operator in a real Hilbert space H with A−1(0) nonempty, and p(t) and r(t) are real-valued functions with appropriate conditions that guarantee the existence of a solution. We prove a weak ergodic th...

We prove that c-cyclically monotone transport plans π optimize the Monge-Kantorovich transportation problem under an additional measurability condition. This measurability condition is always satisfied for finitely valued, lower semi-continuous cost functions. In particular, this yields a positive answer to Problem 2.25 in C. Villani’s book. We emphasize that we do not need any regularity condi...

Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise...

A mixed monotone variational inequality MMVI problem in a Hilbert space H is formulated to find a point u∗ ∈ H such that 〈Tu∗, v − u∗〉 φ v − φ u∗ ≥ 0 for all v ∈ H, where T is a monotone operator and φ is a proper, convex, and lower semicontinuous function onH. Iterative algorithms are usually applied to find a solution of an MMVI problem. We show that the iterative algorithm introduced in the ...

We present an easy to implement drift splitting numerical method for the approximation of stiff, nonlinear stochastic differential equations (SDEs). The method is an adaptation of the semi-implicit backward differential formula (SBDF) multistep method for deterministic differential equations and allows for a semi-implicit discretization of the drift term to remove high order stability constrain...

This paper studies a one-sector optimal growth model with linear utility in which the production function is only required to be increasing and upper semicontinuous. The model also allows for a general form of irreversible investment. We show that every optimal capital path is strictly monotone until it reaches a steady state; further, it either converges to zero, or reaches a positive steady s...

The primary goal of this paper is to shed some light on the maximality of the pointwise sum of two maximal monotone operators. The interesting purpose is to extend some recent results of Attouch, Moudafi and Riahi on the graphconvergence of maximal monotone operators to the more general setting of reflexive Banach spaces. In addition, we present some conditions which imply the uniform Brézis-Cr...

The set of solutions of 1.1 is denoted by A B −1 0 . A number of problems arising in structural analysis, mechanics, and economics can be studied in the framework of this kind of variational inclusions; see, for instance, 1–4 . The problem 1.1 includes many problems as special cases. 1 If B ∂φ : H → 2 , where φ : H → R ∪ ∞ is a proper convex lower semicontinuous function and ∂φ is the subdif an...

In this paper we construct a conservative Markov semi-group with generator L = Δ + b ⋅ ∇ on R n , where is divergence-free vector field which belongs to 2 ∩ p < . The research motivated by the question of understanding blow-up solutions fluid dynamic equations, attracts lot attention in recent years.