We establish Liouville-type theorems for stable and finite Morse index weak solutions of −∆pu = f(x)F (u) in R . For a general non-linearity F ∈ C(R) and f(x) = |x|, we prove such theorems in dimensions N ≤ 4(p+α) p−1 +p, for bounded radial stable solutions. Then, we give some point-wise estimates for not necessarily bounded solutions. Also, similar theorems will be proved for both radial finit...

This thesis studies axiomatic and computational aspects of set-valued solution concepts in social choice and game theory. It is divided into two parts. The first part focusses on solution concepts for normal-form games that are based on varying notions of dominance. These concepts are intuitively appealing and admit unique minimal solutions in important subclasses of games. Examples include Sha...

Given a preference system (G, ≺) and an integral weight function defined on the edge set of G (not necessarily bipartite), the maximum-weight stable matching problem is to find a stable matching of (G, ≺) with maximum total weight. We study this N P-hard problem using linear programming and polyhedral approaches, and show that the Rothblum system for defining the fractional stable matching poly...