相关论文: Massera Type Theorem for Abstract Functional Diffe…

This work is devoted to present Massera-type theorems for the Kawahara system, a higher order dispersive equation, posed in a bounded domain. Precisely, thanks to some properties of the semigroup and the decays of the solutions of this…

This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…

In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…

Motivated by Lazer-Leach type results, we study the existence of periodic solutions for systems of functional-differential equations at resonance with an arbitrary even-dimensional kernel and linear deviating terms involving a general delay…

We prove results of existence of a solution (resp. existence and uniqness of a solution) for nonlinear differential equations of type $x'(t) +G(x,t) x(t) = F(x,t),$ in an abstract Banach subspace $X$ of the space of bounded real-valued…

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 $E$, $$u'(t)+Au(t)=F(t,u(t),u(t-\tau)),\ \ \ \ t\in\R,$$…

Let $F(u)=h$ be an operator equation in a Banach space $X$, $\|F'(u)-F'(v)\|\leq \omega(\|u-v\|)$, where $\omega\in C([0,\infty))$, $\omega(0)=0$, $\omega(r)>0$ if $r>0$, $\omega(r)$ is strictly growing on $[0,\infty)$. Denote…

In this paper we are concerned with existence results for a coupled system of quadratic functional differential equations. This system is reduced to a fixed point problem for a block operator matrix with nonlinear inputs. To prove the…

An evolution problem for abstract differential equations is studied. The typical problem is: $$\dot{u}=A(t)u+F(t,u), \quad t\geq 0; \,\, u(0)=u_0;\quad \dot{u}=\frac {du}{dt}\qquad (*)$$ Here $A(t)$ is a linear bounded operator in a Hilbert…

We are concerned with some extensions of the classical Liouville theorem for bounded harmonic functions to solutions of more general equations. We deal with entire solutions of periodic and almost periodic parabolic equations including the…

In this paper we study the existence of solution for the following class of nonlocal problems \[ L_0u =f(x,u)+g(x) , \ \mbox{in} \ \Omega, \] where $\Omega \subset \mathbb{R}^{N}$, $N\geq 1$, is a bounded connected open, $g \in…

In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in&…

Differential equations with state-dependent delays define a semiflow of continuously differentiable solution operators in general only on the associated {\it solution manifold} in the Banach space $C^1_n=C^1([-h,0],\mathbb{R}^n)$. For a…

We consider the numerical solution of the equation - \Delta u - f(u) = g, for the unknown u satisfying Dirichlet conditions in a bounded domain. The nonlinearity f has bounded, continuous derivative. The algorithm uses the finite element…

In the paper a new numerical-analytical method for solving the Cauchy problem for systems of ordinary differential equations of special form is presented. The method is based on the idea of the FD-method for solving the operator equations…

In this paper we study the dynamical behaviour of the differential equation \begin{equation*} x''+ax^+ -bx^-=f(t), \end{equation*} where $x^+=\max\{x,0\}$,\ $x^-=\max\{-x,0\}$, $a$ and $b$ are two different positive constants, $f(t)$ is a…

Using model theory and differential algebra, we give necessary conditions for algebraic ordinary differential equations to have a complex Pfaffian solution on some complex domain. These tools also allow us to give many examples of algebraic…

We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(\theta, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type…

Behavior of solutions of $f''+Af=0$ is discussed under the assumption that $A$ is analytic in $\mathbb{D}$ and $\sup_{z\in\mathbb{D}}(1-|z|^2)^2|A(z)|<\infty$, where $\mathbb{D}$ is the unit disc of the complex plane. As a main result it is…

We are concerned with the almost automorphic solutions to the second-order elliptic differential equations of type $\ddot u(s) + 2 B \dot u(s) + A u(s) = f(s) (\ast),$ where $A, B$ are densely defined closed linear operators acting in a…