In this paper, for solving the finite-dimensional variational inequality problem ðx x ÞFðx ÞP0; 8x 2 X; where F is a C ðr > 1Þ mapping from X to R, X 1⁄4 fx 2 R : gðxÞO0g is nonempty (not necessarily bounded) and gðxÞ :R ! R is a convex Crþ1 mapping, a homotopy method is presented. Under various conditions, existence and convergence of a smooth homotopy path from almost any interior initial poi...

We give a simple proof of existence of solutions of the dispersion management and diffraction management equations for zero average dispersion, respectively diffraction. These solutions are found as maximizers of non-linear and non-local variational problems which are invariant under a large non-compact group. Our proof of existence of maximizer is rather direct and avoids the use of Lions’ con...

Treating games of incomplete information with countable sets of actions and types and finite but large player sets we demonstrate that for every mixed strategy profile there is a pure strategy profile that is ‘εequivalent’. Our framework introduces and exploits a distinction between crowding attributes of players (their external effects on others) and their taste attributes (their payoff functi...

We give an elementary proof of existence and uniqueness of Gibbs states for Hölder weight systems on subshifts of finite type. This uses a notion of duality for such subshifts. The approach of Paterson [2] is used to construct a measure with a prescribed Jacobian and the duality is used to produce an invariant measure from this

By variational methods, we provide a simple proof of existence of a heteroclinic orbit to the Hamiltonian system u�� = ∇W (u) that connects the two global minima of a double-well potential W . Moreover, we consider several inhomogeneous extensions.

This paper is concerned with the transient dynamics described by the solutions of the reaction-diffusion equations in which the reaction term consists of a combination of a superlinear power-law absorption and a time-independent point source. In one space dimension, solutions of these problems with zero initial data are known to approach the stationary solution in an asymptotically self-similar...

where T1, . . . , Tn, S1, . . . , Sn : [a, b] → R. (2) Suppose K 6= 0. Then we may consider each of the systems {T1, . . . , Tn}, {S1, . . . , Sn} linearly independent. Indeed, starting from an expression of kind (1), we consequently reduce the number of items while it is needed. Assume that we need to express the functions (2) in terms of K. In order to do it, we find such points (a proof of e...

In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.