Degenerate and Singular Evolution Equations in Banach Space.
Degenerate differential operators with parameters.
Dependence of a weak solution of the first order differential equation on a parameter.
Derivative of the norm of a linear mapping and its application to differential equations
In this paper the notion of the derivative of the norm of a linear mapping in a normed vector space is introduced. The fundamental properties of the derivative of the norm are established. Using these properties, linear differential equations in a Banach space are studied and lower and upper estimates of the norms of their solutions are derived.
Dérivées intermédiaires dans les espaces de Hilbert pondérés. Application au comportement à l’ des solutions des équations d’évolution
Deterministic homogenization of parabolic monotone operators with time dependent coefficients.
Differential Equations in Abstract Cones
We extend the method of quasilinearization to differential equations in abstract normal cones. Under some assumptions, corresponding monotone iterations converge to the unique solution of our problem and this convergence is superlinear or semi–superlinear
Differential equations in banach space and henstock-kurzweil integrals
In this paper, using the properties of the Henstock-Kurzweil integral and corresponding theorems, we prove the existence theorem for the equation x' = f(t,x) and inclusion x' ∈ F(t,x) in a Banach space, where f is Henstock-Kurzweil integrable and satisfies some conditions.
Differential equations in metric spaces
Differential equations in metric spaces
We give a meaning to derivative of a function , where is a complete metric space. This enables us to investigate differential equations in a metric space. One can prove in particular Gronwall’s Lemma, Peano and Picard Existence Theorems, Lyapunov Theorem or Nagumo Theorem in metric spaces. The main idea is to define the tangent space of . Let , be continuous at zero. Then by the definition and are in the same equivalence class if they are tangent at zero, that is if By we denote...
Differential Equations in Operator Algebras. I. Invariance of the Siegel Disk.
Differential inclusions and multivalued integrals
In this paper we consider the nonlocal (nonstandard) Cauchy problem for differential inclusions in Banach spaces x'(t) ∈ F(t,x(t)), x(0)=g(x), t ∈ [0,T] = I. Investigation over some multivalued integrals allow us to prove the existence of solutions for considered problem. We concentrate on the problems for which the assumptions are expressed in terms of the weak topology in a Banach space. We recall and improve earlier papers of this type. The paper is complemented...
Differential operators with non dense domain
Differential subordination results for new classes of the family .
Differential-algebraic equations in the theory of invariant manifolds for singular equations.
Diffusion phenomenon for second order linear evolution equations
We present an abstract theory of the diffusion phenomenon for second order linear evolution equations in a Hilbert space. To derive the diffusion phenomenon, a new device developed in Ikehata-Matsuyama [5] is applied. Several applications to damped linear wave equations in unbounded domains are also given.
Discrete methods and exponential dichotomy of semigroups.
Discretization methods for nonconvex differential inclusions.