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

This paper deals with the following Cauchy problem to nonlinear time fractional non-autonomous integro-differential evolution equation of mixed type via measure of noncompactness $$ \left\{\begin{array}{ll} ^CD^{\alpha}_tu(t)+A(t)u(t)=…

In this article, first we give a general lemma on the existence of regular homeomorphic solutions $f$ with the hydrodynamic normalization $f(z)=z+o(1)$ as $z\to\infty$ to the degenerate Beltrami equations $\overline{\partial}f=\mu\,\partial…

Let $F$ be a nonlinear Frechet differentiable map in a real Hilbert space. Condition sufficient for existence of a solution to the equation $F(u)=0$ is given, and a method (dynamical systems method, DSM) to calculate the solution as the…

In this article we introduce a class of discontinuous almost automorphic functions which appears naturally in the study of almost automorphic solutions of differential equations with piecewise constant argument. Their fundamental properties…

The segmented formulation of the Tau method is used to numerically solve the non-autonomous forward-backward functional differential equation x'(t) = a(t)x(t) + b(t)x(t-1) + c(t)x(t+1), where x is the unknown function, a, b, and c are known…

Assume that $Au=f,\quad (1)$ is a solvable linear equation in a Hilbert space $H$, $A$ is a linear, closed, densely defined, unbounded operator in $H$, which is not boundedly invertible, so problem (1) is ill-posed. It is proved that the…

Our paper focuses on investigating the existence and possible forms of solutions to the nonlinear differential equation \beas f^m+\big(Rf^{(k)}\big)^n=Qe^{\alpha},\eeas where where $k$, $m$ and $n$ are three positive integers, $Q$ and $R$…

We consider a second order nonlinear ordinary differential equation of the form $u'' + f(u) = p(t)$ where the forcing term $p(t)$ is a $T$-periodic function and the nonlinearity $f(u)$ satisfies the properties of Ambrosetti-Prodi problems.…

We consider the Banach space $H^\infty_{\mathrm{ap}}(\mathbb{C}_0)$ of bounded analytic functions on the open right half-plane $\mathbb{C}_0$ that are almost periodic on some smaller half-plane, as well as the subspace…

We consider the following quasi-linear parabolic system of backward partial differential equations: $(\partial_t+L)u+f(\cdot,\cdot,u, \nabla u\sigma)=0$ on $[0,T]\times \mathbb{R}^d\qquad u_T=\phi$, where $L$ is a possibly degenerate second…

Let $X$ and $Y$ be compact K\"ahler manifolds of dimension $3$. A bimeromorphic map $f:X\rightarrow Y$ is pseudo-isomorphic if $f:X-I(f)\rightarrow Y-I(f^{-1})$ is an isomorphism. Let $T=T^+-T^-$ be a current on $Y$, where $T^{\pm}$ are…

We consider the equation $\Delta_x u+u_{yy}+f(u)=0,\ x=(x_1,\dots,x_N)\in\mathbb{R}^N,\ y\in \mathbb{R},$ where $N\geq 2$ and $f$ is a sufficiently smooth function satisfying $f(0)=0$, $f'(0)<0$, and some natural additional conditions. We…

We show how the approach of Yosida approximation of the derivative serves to obtain new results for evolution systems. Using this method we obtain multivalued time dependent perturbation results. Additionally, translation invariant…

In this paper, we first propose a single-species system with impulsive effects on time scales and by establishing some new comparison theorems of impulsive dynamic equations on time scales, we obtain sufficient conditions to guarantee the…

We consider positive solutions, possibly unbounded, to the semilinear equation $-\Delta u=f(u)$ on continuous epigraphs bounded from below. Under the homogeneous Dirichlet boundary condition, we prove new monotonicity results for $u$, when…

Assume that $$ Au=f,\quad (1) $$ is a solvable linear equation in a Hilbert space, $||A||<\infty$, and $R(A)$ is not closed, so problem (1) is ill-posed. Here $R(A)$ is the range of the linear operator $A$. A DSM (dynamical systems method)…

We are interested in the differential equation $\ddot u(t) = -A u(t) - c A \dot u(t) + \lambda u(t) + F(t,u(t))$, where $c > 0$ is a damping factor, $A$ is a sectorial operator and $F$ is a continuous map. We consider the situation where…

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to…

We prove the well-posedness of the differential equation $Au=f$ in the setting of a stratified group $\mathbb{G}$ when the considered second-order differential operator $A$ can be non-invariant and non-linear. Our approach follows the…

This paper continues an earlier work on the structure of solutions to two classes of functional equation. Let $Z$ be a compact Abelian group and $U_1$, \ldots, $U_k \leq Z$ be closed subgroups. Given $f:Z\to\mathbb{T}$ and $w \in Z$, one…