Normal solvability, solvability and fixed-point theorems

Some Solvability Theorems for Nonlinear Equations

Let E be a locally convex space and f : E → E a mapping. We say that the equation f(x) = 0 is almost solvable on A ⊂ E if 0 ∈ f(A). In this paper some results about the solvability and almost solvability are given. Our results are based on some classical fixed point theorems and on some geometrical conditions.

Normal Solvability of General Linear Elliptic Problems

The paper is devoted to general elliptic problems in the Douglis-Nirenberg sense. We obtain a necessary and sufficient condition of normal solvability in the case of unbounded domains. Along with the ellipticity condition, proper ellipticity and Lopatinsky condition that determine normal solvability of elliptic problems in bounded domains, one more condition formulated in terms of limiting prob...

Group Solvability

A Theory of Solvability for Lossless Power Flow Equations – Part I: Fixed-Point Power Flow

This two-part paper details a theory of solvability for the power flow equations in lossless power networks. In Part I, we derive a new formulation of the lossless power flow equations, which we term the fixed-point power flow. The model is stated for both meshed and radial networks, and is parameterized by several graph-theoretic matrices – the power network stiffness matrices – which quantify...

A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes

This note demonstrates that a lattice game with strategic substitutes is dominancesolvable if and only if there exists a unique fixed point of the function that results from an iteration of the best response function. This finding complements a result of Milgrom and Roberts’ (1990) by which a lattice game with strategic complements is dominance-solvable if and only if there exists a unique Nash...