Existence Results for Differential Inclusions with Nonlinear Growth Conditions in Banach Spaces

In the Banach space setting, the existence of viable solutions for differential inclusions with nonlinear growth; that is, ẋ(t)∈F(t,x(t)) a.e. on I, x(t)∈S, ∀t∈I, x(0)=x0∈S, (*), where S is a closed subset in a Banach space , I=[0,T], (T>0), F:I×S→, is an upper semicontinuous set-valued mapping with convex values satisfying F(t,x)⊂c(t)x+xp, ∀(t,x)∈I×S, where p∈ℝ, with p≠1, and c∈C([0,T],ℝ+). The existence of solutions for nonconvex sweeping processes with perturbations with nonlinear growth is also proved in separable Hilbert spaces

Optimal Harvesting Effort for Nonlinear Predictive Control Model for a Single Species Fishery

We use nonlinear model predictive control to find the optimal harvesting effort of a renewable resource system with a nonlinear state equation that maximizes a nonlinear profit function. A solution approach is proposed and discussed and satisfactory numerical illustrations are provided

Iterative Methods for Nonconvex Equilibrium Problems in Uniformly Convex and Uniformly Smooth Banach Spaces

We suggest and study the convergence of some new iterative schemes for solving nonconvex equilibrium problems in Banach spaces. Many existing results have been obtained as particular cases

Inégalités variationnelles non convexes

Dans cet article nous proposons différents algorithmes pour résoudre une nouvelle classe de problèmes variationels non convexes. Cette classe généralise plusieurs types d'inégalités variationnelles (Cho et al. (2000), Noor (1992), Zeng (1998), Stampacchia (1964)) du cas convexe au cas non convexe. La sensibilité de cette classe de problèmes variationnels non convexes a été aussi étudiée

Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions

We prove a new result of existence of equilibria for an u.s.c. set-valued mapping on a compact set of R which is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mapping ( ) − . The main point of our result lies in the fact that we do not impose the usual tangential condition in terms of the Clarke tangent cone. Illustrative examples are stated showing the importance of our results and that the existence of such equilibria does not need necessarily such usual tangential condition

Subdifferential Properties of Minimal Time Functions Associated with Set-Valued Mappings with Closed Convex Graphs in Hausdorff Topological Vector Spaces

For a set-valued mapping M defined between two Hausdorff topological vector spaces E and F and with closed convex graph and for a given point (x,y)∈E×F, we study the minimal time function associated with the images of M and a bounded set Ω⊂F defined by M,Ω(x,y):=inf{t≥0:M(x)∩(y+tΩ)≠∅}. We prove and extend various properties on directional derivatives and subdifferentials of M,Ω at those points of (x,y)∈E×F (both cases: points in the graph gph M and points outside the graph). These results are used to prove, in terms of the minimal time function, various new characterizations of the convex tangent cone and the convex normal cone to the graph of M at points inside gph M and to the graph of the enlargement set-valued mapping at points outside gph M. Our results extend many existing results, from Banach spaces and normed vector spaces to Hausdorff topological vector spaces (Bounkhel, 2012; Bounkhel and Thibault, 2002; Burke et al., 1992; He and Ng, 2006; and Jiang and He 2009). An application of the minimal time function M,Ω to the calmness property of perturbed optimization problems in Hausdorff topological vector spaces is given in the last section of the paper

Mathematical modeling and numerical simulations of the motion of nanoparticles in straight tube

Nanotechnology is a very important field in science and technology, and research projects in this domain attract considerable funding. The existing research works in nanotechnology deal with chemical, physical, and biological issues or a combination of these fields, but very small number of works has been undertaken on mathematical modeling. Mathematical models can greatly reduce the time involved in experimentation, which in turn reduces the research cost. In this article, we consider the mathematical modeling of the motion of nanoparticles in a viscous flow inside straight tube. Illustrative simulations of the model are provided

Existence of Equilibria and Fixed Points of Set-Valued Mappings on Epi-Lipschitz Sets with Weak Tangential Conditions

We prove a new result of existence of equilibria for an u.s.c. set-valued mapping F on a compact set S of Rn which is epi-Lipschitz and satisfies a weak tangential condition. Equivalently this provides existence of fixed points of the set-valued mapping x⇉F(x)-x. The main point of our result lies in the fact that we do not impose the usual tangential condition in terms of the Clarke tangent cone. Illustrative examples are stated showing the importance of our results and that the existence of such equilibria does not need necessarily such usual tangential condition