We present two types of perturbations with reverse effects on some scalar fully nonlinear second order elliptic differential operators: on the other hand, first order perturbations which destroy the global solvability of the Dirichlet problem, in smooth bounded domains of Rn; on the other hand, an integral perturbation which restore the local solvability, on compact connected manifolds without ...

We provide polynomial time algorithms for deciding equation solvability and identity checking over groups that are semidirect products of two nite Abelian groups. Our main method is to reduce these problems to the sigma equation solvability and sigma equivalence problems over modules for commutative unital rings.

In this paper we will give an outline of the proof of the solvability of the halting and reachability problem for 2-symbolic tag systems with a deletion number v = 2. This result will be situated in a more general context of research on limits of solvability in tag systems.

This article analyzes the solvability of second-order, nonlinear dynamic boundary value problems (BVPs) on time scales. New Bernstein-Nagumo conditions are developed that guarantee an a priori bound on the delta derivative of potential solutions to the BVPs under consideration. Topological methods are then employed to gain solvability.

For the functional differential equation u(n)(t) = f(u)(t) we have established the sufficient conditions for solvability and unique solvability of the boundary value problems u(i)(0) = ci (i = 0, . . . , m− 1), ∫ +∞ 0 |u(m)(t)|2dt < +∞ and u(i)(0) = ci (i = 0, . . . , m− 1),

The pure lambda calculus has a well-established ‘standard theory’ in which the notion of solvability characterises the operational relevance of terms. Solvable terms, defined as solutions to a beta-equation, have a ‘syntactic’ characterisation as terms with head normal form. Unsolvable terms are irrelevant and can be beta-equated without affecting consistency. The derived notions of sensibility...

A finite group $G$ is called rational if all its irreducible complex characters are rational valued. In this paper we discuss about rational groups with Sylow 2-subgroups of nilpotency class at most 2 by imposing the solvability and nonsolvability assumption on $G$ and also via nilpotency and nonnilpotency assumption of $G$.

This paper surveys recent work on quasi-exactly solvable Schrr odinger operators and Lie algebras of diierential operators.