Lp-solutions to BSDEs with super-linear growth coefficient. Application to degenerate semilinear PDEs.

We consider multidimensional backward stochastic differential equations (BSDEs). We prove the existence and uniqueness of solutions when the coefficient grow super-linearly, and moreover, can be neither locally Lipschitz in the variable y nor in the variable z. This is done with super-linear growth coefficient and a p-integrable terminal condition (p & 1). As application, we establish the existence and uniqueness of solutions to degenerate semilinear PDEs with superlinear growth generator and an Lp-terminal data, p & 1. Our result cover, for instance, the case of PDEs with logarithmic nonlinearities.

Stable rank of leavitt path algebra

We characterize the values of the stable rank for Leavitt path algebras, by giving concrete criteria in terms of properties of the underlying graph.

Multiplicity of limit cycles and analytic m-solutions for planar differential systems

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Stability of periodic solutions obtained via the averaging method for nonsmooth Lipschitz system

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Political autonomy and independence: theory and experimental evidence

We study the process by which subordinated regions of a country can obtain a more favourable political status. In our theoretical model a dominant and a dominated region first interact through a voting process that can lead to different degrees of autonomy. If this process fails then both regions engage in a costly political conflict which can only lead to the maintenance of the initial subordination of the region in question or to its complete independence. In the subgame-perfect equilibrium the voting process always leads to an intermediate arrangement acceptable for both parts. Hence, the costly political struggle never occurs. In contrast, in our experiments we observe a large amount of fighting involving high material losses, even in a case in which the possibilities for an arrangement without conflict are very salient. In our experimental environment intermediate solutions are feasible and stable, but purely emotional elements prevent them from being reached.

Corrigendum: stable matchings and preferences of couples

We correct an omission in the definition of the domain of weakly responsive preferences introduced in Klaus and Klijn (2005) or KK05 for short. The proof of the existence of stable matchings (KK05, Theorem 3.3) and a maximal domain result (KK05, Theorem 3.5) are adjusted accordingly.

The existence of periodic solutions of a two dimensional Lattice

We consider a two dimensional lattice coupled with nearest neighbor interaction potential of power type. The existence of infinite many periodic solutions is shown by using minimax methods.

Efficient and stable collective choices under gregarious preferences

We consider collective choice problems where a set of agents have to choose an alternative from a finite set and agents may or may not become users of the chosen alternative. An allocation is a pair given by the chosen alternative and the set of its users. Agents have gregarious preferences over allocations: given an allocation, they prefer that the set of users becomes larger. We require that the final allocation be efficient and stable (no agent can be forced to be a user and no agent who wants to be a user can be excluded). We propose a two-stage sequential mechanism whose unique subgame perfect equilibrium outcome is an efficient and stable allocation which also satisfies a maximal participation property.

Strong solutions for stochastic porous media equations with jumps

We prove global well-posedness in the strong sense for stochastic generalized porous media equations driven by locally square integrable martingales with stationary independent increments.

Positive solutions of nonlinear problems involving the square root of the Laplacian

We consider nonlinear elliptic problems involving a nonlocal operator: the square root of the Laplacian in a bounded domain with zero Dirichlet boundary conditions. For positive solutions to problems with power nonlinearities, we establish existence and regularity results, as well as a priori estimates of Gidas-Spruck type. In addition, among other results, we prove a symmetry theorem of Gidas-Ni-Nirenberg type.

Condensation of polyhedric structures onto soap films

We study the existence of solutions to general measure-minimization problems over topological classes that are stable under localized Lipschitz homotopy, including the standard Plateau problem without the need for restrictive assumptions such as orientability or even rectifiability of surfaces. In case of problems over an open and bounded domain we establish the existence of a “minimal candidate”, obtained as the limit for the local Hausdorff convergence of a minimizing sequence for which the measure is lower-semicontinuous. Although we do not give a way to control the topological constraint when taking limit yet— except for some examples of topological classes preserving local separation or for periodic two-dimensional sets — we prove that this candidate is an Almgren-minimal set. Thus, using regularity results such as Jean Taylor’s theorem, this could be a way to find solutions to the above minimization problems under a generic setup in arbitrary dimension and codimension.

International Institutions as Solutions to Underlying Games of Cooperation

This Working Paper was presented at the international workshop "Game Theory in International Relations at 50", organized and coordinated by Professor Jacint Jordana and Dr. Yannis Karagiannis at the Institut Barcelona d'Estudis Internacionals on May 22, 2009. The day-long Workshop was inspired by the desire to honour the ground-breaking work of Professor Thomas Schelling in 1959-1960, and to understand where the discipline International Relations lies today vis-à-vis game theory.

Stable stationary states of non-local interaction equations

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A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.