We elucidate a powerful yet simple method for deriving comparative statics conclusions for a wide variety of models: Monotone Comparative Statics (Milgrom and Shannon 1994). Monotone comparative static methods allow researchers to extract robust, substantive empirical implications from formal models that can be tested using ordinal data and simple nonparametric tests. When these methods apply, ...

This paper deals with the existence and uniqueness of the classical solution of Fourier’s first problem for a wide class of systems of two weakly coupled quasi-linear second order partial differential functional equations. One equation is of the parabolic type (the degenerated parabolic equation) and the other of the elliptic type (the elliptic equation with a parameter). The functional depende...

Strongly Fejér monotone mappings are widely used to solve convex problems by corresponding iterative methods. Here the maximal of such mappings with respect to set inclusion of the images are investigated. These mappings supply restriction zones for the successors of Fejér monotone iterative methods. The basic tool is the representation of the images by intersection of certain balls.

In this paper, a boundary value problem for a nonlinear second-order ordinary differential equation is studied. By means of the maximum principle we established the existence and the uniqueness of a solution of the problem. Then for finding the solution an iterative method is proposed. It is proved that this method converges much faster than the Picar successive approximations and in a particul...

We introduce and study a class of a system of random set-valued variational inclusion problems. Some conditions for the existence of solutions of such problems are provided, when the operators are contained in the classes of generalized monotone operators, so-called A,m, η -monotone operator. Further, the stability of the iterative algorithm for finding a solution of the considered problem is a...

In this paper a second order monotone numerical method is constructed for a singularly perturbed ordinary differential equation with two small parameters affecting the convection and diffusion terms. The monotone operator is combined with a piecewise-uniform Shishkin mesh. An asymptotic error bound in the maximum norm is established theoretically whose error constants are show to be independent...

We consider systems of ODEs that describe the dynamics of particles. Each particle satisfies a Newton law (including a damping term and an acceleration term) where the force is created by the interactions with other particles and with a periodic potential. The presence of a damping term allows the system to be monotone. Our study takes into account the fact that the particles can be different. ...

First we discuss the description of inverse polynomial images of [−1, 1], which consists of two Jordan arcs, by the endpoints of the arcs only. The polynomial which generates the two Jordan arcs is given explicitly in terms of Jacobi’s theta functions. Then the main emphasis is put on the case where the two arcs are symmetric with respect to the real line. For instance it is demonstrated that t...

We study nonparametric isotonic confidence intervals for monotone functions. In [1] pointwise confidence intervals, based on likelihood ratio tests for the restricted and unrestricted MLE in the current status model, are introduced. We extend the method to the treatment of other models with monotone functions, and demonstrate our method by a new proof of the results in [1] and also by construct...

‎‎in this paper‎, ‎the existence and uniqueness of positive solutions for a class of nonlinear initial value problem for a finite fractional difference equation obtained by constructing the upper and lower control functions of nonlinear term without any monotone requirement‎ .‎the solutions of fractional difference equation are the size of tumor in model tumor growth described by the gompertz f...