On general solvability properties of $p$-Lapalacian-like equations

ON GENERAL SOLVABILITY PROPERTIES OF p-LAPALACIAN-LIKE EQUATIONS

We discuss how the choice of the functional setting and the definition of the weak solution affect the existence and uniqueness of the solution to the equation −∆pu = f in Ω, where Ω is a very general domain in N , including the case Ω = N .

Indices and solvability for general systems of differential equations

Solvability of Diophantine Equations

Attila Bérczes (University of Debrecen): On arithmetic properties of solutions of norm form equations. Abstract. Let α be an algebraic number of degree n and K := Q(α). Consider the norm form equation NK/Q(x0 + x1α+ x2α + . . .+ xn−1α) = b in x0, . . . , xn−1 ∈ Z. (1) Let H denote the solution set of (1). Arranging the elements of H in an |H| × n array H, one may ask at least two natural questi...

On the Solvability of Magnetic Differential Equations

The calculation of both resistive and ideal plasma equilibria amounts to solving a number of magnetic differential equations which are of the type ~ B ·∇Φ = s. We apply the necessary and sufficient criterion for the existence of the potential Φ and find that a static equilibrium configuration of a magnetically confined plasma does not exist in axi-symmetric toroidal geometry. AMS classification...

On Nash-solvability of chess-like games

In 2003, the first two authors proved that a chess-likes game has a Nash equilibrium (NE) in pure stationary strategies if (A) the number n of players is at most 2, or (B) the number p of terminals is at most 2 and (C) any infinite play is worse than each terminal for every player. In this paper we strengthen the bound in (B) replacing p ≤ 2 by p ≤ 3, provided (C) still holds. On the other hand...