Related papers: Note on the existence theory for evolution equatio…
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational…
We present an understandable, efficient, and streamlined proof of the Holonomy Decomposition for finite transformation semigroups and automata. This constructive proof closely follows the existing computational implementation. Its novelty…
We provide a concise introduction to the symmetry approach to integrability. Some results on integrable evolution and systems of evolution equations are reviewed. Quasi-local recursion and Hamiltonian operators are discussed. We further…
This paper is the second part of our series of works to establish $L^2$ estimates and existence theorems for the $\overline{\partial}$ operators in infinite dimensions. In this part, we consider the most difficult case, i.e., the underlying…
We study abstract linear and nonlinear evolutionary systems with single or multiple delay feedbacks, illustrated by several concrete examples. In particular, we assume that the operator associated with the undelayed part of the system…
We study generalized solutions of an evolutionary equation related to a densely defined skew-symmetric operator in a real Hilbert space. We establish existence of a contractive semigroup, which provides generalized solutions, and find…
An abstract framework for the theory of statistical solutions is developed for general evolution equations, extending the theory initially developed for the three-dimensional incompressible Navier-Stokes equations. The motivation for this…
We carry out an analysis of the existence of solutions for a class of nonlinear partial differential equations of parabolic type. The equation is associated to a nonlocal initial condition, written in general form which includes, as…
The Lax-Phillips scattering theory is an appealing abstract framework for the analysis of scattering resonances. Quantum mechanical adaptations of the theory have been proposed. However, since these quantum adaptations essentially retain…
There are three main results in this paper. First, we find an easily computable and simple condition which is necessary and sufficient for a commuting tuple of contractions to possess a non-zero Toeplitz operator. This condition is just…
We present an existence theory for martingale and strong solutions to doubly nonlinear evolution equations in a separable Hilbert space in the form $$d(Au) + Bu\,dt \ni F(u)\,dt + G(u)\,dW$$ where both $A$ and $B$ are maximal monotone…
This paper is devoted to the study of traveling waves for monotone evolution systems of bistable type. Under an abstract setting, we establish the existence of bistable traveling waves for discrete and continuous-time monotone semiflows.…
In this paper we study quasilinear elliptic systems driven by so-called double phase operators and nonlinear right-hand sides depending on the gradients of the solutions. Based on the surjectivity result for pseudomonotone operators we…
We give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.
We consider evolution equation with fractional Schr\"odinger operators in Morrey spaces. We prove order preserving properties of the associated semigroup in Morrey scale. We prove monotonicity of the semigroup with respect to Morrey's…
We briefly review the use of unitary evolution as a uniqueness criterion in the selection of quantum representations, in the context of scalar fields in non-stationary situations.
Finding necessary and sufficient conditions for isomorphism between two semigroups of order-preserving transformations over an infinite domain with restricted range was an open problem in \cite{FHQS}. In this paper, we show a proof strategy…
In this paper, we prove several generalizations and applications of a fixed point theorem. This theorem is used to prove the existence and uniqueness of solutions of the linear sparse matrix problem considered.
The aim of this paper is to give an existence result for a class of one-dimensional, non-convex, non-coercive problems in the Calculus of Variations. The main tools for the proof are an existence theorem in the convex case and the closure…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…