In this paper we use two global inversion theorems to establish the existence and uniqueness for a nonlinear second order homogeneous Dirichlet system.

We prove the existence and uniqueness of solutions to the timedependent incompressible Navier-Stokes equations with a free-boundary governed by surface tension. The solution is found using a topological fixed-point theorem that requires the analysis of a model linear problem consisting of the time-dependent Stokes equation with linearized mean-curvature forcing on the boundary. We use energy me...

We show a reduction of Hilbert’s tenth problem to the solvability of the matrix equation A1 1 A i2 2 · · ·A ik k = Z over non-commuting integral matrices, where Z is the zero matrix, thus proving that the solvability of the equation is undecidable. This is in contrast to the case whereby the matrix semigroup is commutative in which the solvability of the same equation was shown to be decidable ...

The paper aims at formulating an integrated approach for the selection of decentralized control structures using a number of structural criteria aiming at facilitating the design of decentralised control schemes. This requires the selection of decentralisation structure that will allow the generic solvability of a variety of decentralised control problems, such as pole assignment by decentralis...

Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from the viewpoint of logical (inter-)definability. All problems that we consider are decidable in polynomial time, but not expressible in fixedpoint ...

We introduce an alternative concept to determine the solvability of two-player games with perfect information. This concept — based on games currently solved — claims that the applicable solving procedures have a significant influence on the solvability of games. This contrasts with current views that suggest that solvability is related to state-space and game-tree complexity. Twenty articles o...

This work is devoted to study the existence and uniqueness of solution an analogue Gellerstedt problem with nonlocal assumptions on boundary integral gluing conditions for parabolic-hyperbolic type equation nonlinear terms Gerasimov–Caputo operator differentiation. Using method energy, have been proved. Existence was proved by successive approximations factorial law Volterra equations.

The classical approach of solvability using group theory is well known and one original motivation is to solve polynomials by radicals. Radicals are square, cube, square root, cube root etc of the original coefficients for the polynomial. A polynomial is solvable by radicals if the permutation group is solvable. This is exact solvability via group theory. With modern computers, we might need to...

In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.