Related papers: Almost Periodic Solutions of Evolution Differentia…
A semilinear wave equation with slowly varying wave speed is considered in one to three space dimensions on a bounded interval, a rectangle or a box, respectively. It is shown that the action, which is the harmonic energy divided by the…
In this paper we develop a method to solve evolution equations on Gelfand triples with time-fractional derivative based on monotonicity techniques. Applications include deterministic and stochastic quasi-linear partial differential…
In this manuscript, we have considered the system governed by a noninstantaneous impulsive dynamical system of integer order with classical and nonlocal conditions and derived sufficient conditions for the trajectory controllability of the…
We characterize the behavior of the solutions of linear evolution partial differential equations on the half line in the presence of discontinuous initial conditions or discontinuous boundary conditions, as well as the behavior of the…
The concept of nonlinear split ordered variational inequality problems on partially ordered vector spaces is a natural extension of linear split vector variational inequality problems on Banach spaces. The results about nonlinear split…
We investigate variational problems with recursive integral functionals governed by infinite-dimensional differential inclusions with an infinite horizon and present an existence result in the setting of nonreflexive Banach spaces. We find…
Stochastic partial differential equations (SPDEs) have become a key modelling tool in applications. Yet, there are many classes of SPDEs, where the existence and regularity theory for solutions is not completely developed. Here we…
In this paper, we discuss the existence and asymptotic stability of the positive periodic mild solutions for the abstract evolution equation with delay in an ordered Banach space $E$, $$u'(t)+Au(t)=F(t,u(t),u(t-\tau)),\ \ \ \ t\in\R,$$…
Dynamical systems that are subject to continuous uncertain fluctuations can be modelled using Stochastic Differential Equations (SDEs). Controlling such system results in solving path constrained SDEs. Broadly, these problems fall under the…
We present a geometric formulation of existence of time quasi-periodic solutions. As an application, we prove the existence of quasi-periodic solutions of $b$ frequencies, $b\leq d+2$, in arbitrary dimension $d$ and for arbitrary non…
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.…
We extend bifurcation results of nonlinear eigenvalue problems from real Banach spaces to any neighbourhood of a given point. For points of odd multiplicity on these restricted domains, we establish that the component of solutions through…
A general framework is presented to discuss the approximate solutions of an evolution equation in a Banach space, with a linear part generating a semigroup and a sufficiently smooth nonlinear part. A theorem is presented, allowing to infer…
In this paper, we first give the definition of random almost periodic solutions of random dynamical systems and give some examples. Then, we prove the existence of such random almost periodic solutions. Further, we introduce the definition…
Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…
In this paper, we investigate the existence and finite-time blow-up for the solution of a reaction-diffusion system of semilinear stochastic partial differential equations (SPDEs) subjected to a two-dimensional fractional Brownian motion…
We study the existence of singular separable solutions to a class of quasilinear equations with reaction term. In the 2-dim case, we use a dynamical system approach to construct our solutions.
We study the Cauchy problem for fully nonlinear (stochastic) parabolic partial differential equations. We provide both in deterministic and stochastic case the existence of a maximal defined solution for the problem and we provide suitable…
The main aim of this paper is to introduce and analyze the notions of subspace almost periodicity and subspace weak almost periodicity for $C$-distribution semigroups and $C$-distribution cosine functions in Banach spaces. We continue our…
We consider the two-dimensional Euler equation with periodic boundary conditions. We construct time quasi-periodic solutions of this equation made of localized travelling profiles with compact support propagating over a stationary state…