Related papers: Note on the existence theory for evolution equatio…
In this note we develop a framework which allows to prove an existence result for non-linear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete…
In this note we develop a framework which allows to prove an abstract existence result for non-linear evolution equations involving so-called non-induced operators, i.e., operators which are not prescribed by a time-dependent family of…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
This paper investigates the existence, uniqueness, and regularity of solutions to evolution equations with time-measurable pseudo-differential operators in weighted mixed-norm Sobolev-Lipschitz spaces. We also explore trace embedding and…
Existence, uniqueness and stability of the solutions of linear stochastic evolution equations are investigated. The results obtained are used to prove theorems on solvability of linear second order stochastic partial differential equations…
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
In this paper we prove an abstract theorem which can be used to study the existence of solitons for various dynamical systems described by partial differential equations. We also give an idea of how the abstract theorem can be applied to…
In this paper we consider evolution equations in the abstract Hilbert space under the special conditions imposed on the operator at the right-hand side of the equation. We establish the method that allows us to formulate the existence and…
An approach to stochastic evolution equations based on a simple generalization of known embedding theorems is presented. It allows for the inclusion of problems which have nonlinear non monotone operators. This is used to discuss the…
In this paper we establish an existence result for a quasilinear Kirchhoff equation via a sub and supersolution approach, by using the pseudomonotone operators theory.
In this note we provide a self-contained proof of an existence and uniqueness result for a class of Banach space valued evolution equations with an additive forcing term. The framework of our abstract result includes, for example, finite…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
We prove by means of advanced pseudo-monotonicity methods an abstract existence result for parabolic partial differential equations with $\log$-H\"older continuous variable exponent nonlinearity governed by the symmetric part of a gradient…
In this paper we consider quasilinear elliptic equations with double phase phenomena and a reaction term depending on the gradient. Under quite general assumptions on the convection term we prove the existence of a weak solution by applying…
A system of two operator equations is considered - one of pseudomonotone type and the other of strongly monotone type - both being strongly coupled. Conditions are given that allow to reduce the solvability of this system to a single…
In this paper, we consider evolution problems involving time dependent maximal monotone operators in Hilbert spaces. Existence and relaxation theorems are proved.
We show the existence of solution for some classes of nonlocal problems. Our proof combines the presence of sub and supersolution with the pseudomonotone operators theory.
In this paper we establish the existence and uniqueness of solutions for nonlinear evolution equations on Banach space with locally monotone operators, which is a generalization of the classical result by J.L. Lions for monotone operators.…
Existence theorem is proven for the generating equations of the split involution constraint algebra. The structure of the general solution is established, and the characteristic arbitrariness in generating functions is described.
We establish a set of relations between several quite diverse types of weighted inequalities involving various integral operators and fairly general quasinorm-like functionals which we call sub-monotone. The main result enables one to solve…