Showing papers on "C0-semigroup published in 1988"
242 citations
TL;DR: In this paper, the theory of boundary-value problems for systems of linear and nonlinear ordinary differential equations is discussed, and criteria are given for problems with functional, many-point, and two-point boundary conditions to be solvable and wellposed, as well as methods of finding approximate solutions.
Abstract: This article contains an exposition of fundamental results of the theory of boundary-value problems for systems of linear and nonlinear ordinary differential equations. In particular, criteria are given for problems with functional, many-point, and two-point boundary conditions to be solvable and well-posed, as well as methods of finding approximate solutions. We also examine questions of existence, uniqueness, and stability of periodic and bounded solutions of nonautonomous differential systems.
159 citations
144 citations
89 citations
Book•
30 Aug 1988
62 citations
01 Jan 1988
TL;DR: A characterization of a-Dedekind complete Banach lattices for which every continuous linear operator T: E -+ co is a difference of two positive linear operators from E into co is given in this paper.
Abstract: We give a characterization of those a-Dedekind complete Banach lattices for which every continuous linear operator T: E -+ co is a difference of two positive linear operators from E into co. 1. Preliminary remarks. Let E and F be infinite dimensional Banach lattices. In general, the space L(E, F) of all continuous linear operators from E into F is not a Riesz space (= vector lattice) with respect to the natural order, i.e., T > 0 iff Tx > 0 for x E E+, even if F is Dedekind complete. However, the subspace Lr (E, F) of regular operators, i.e., the subspace consisting of operators which are differences of positive linear operators, is a Riesz space under the "pointwise order" provided F is Dedekind complete. Moreover, L r(E, F) is a Banach lattice for the norm lITI Jr = 11 ITI 11. A characterization of pairs of Banach lattices E, F for which L(E, F) = Lr (E, F) (or L(E,F) _ Lr(E,F), i.e., these spaces are equal and 11TII = IITIIr) is an old problem which, in general, is still not solved. A classical result in this direction says that L(E, F) _ Lr (E, F) whenever F is a Dedekind complete AM-space with a strong unit or E is an AL-space and there exists a positive contractive projection P: F** -, F. Cartwright and Lotz conjectured in [4] that if L(E, F) = Lr(E, F), then E is Riesz isomorphic to an AL-space or F is Riesz isomorphic to an AMspace. They confirmed the conjecture in the case where E* or F contains a closed sublattice Riesz isomorphic to 1P for some p E [1, oo), but Abramovic constructed in [1] a pair of Banach lattices E and F with the following properties: E is not Riesz isomorphic to an AL-space, F is not Riesz isomorphic to an AM-space and for any operator T E L(E, F) the modulus ITI: E -F exists. The identity L(E, F) = Lr (E, F) was also considered in [6] where the author, among other things, gave a characterization of a compact set X provided L(C(X), C(Y)) = Lr(C(X), C(Y)) for every compact set Y. The space 11(A) is the unique Banach lattice E (up to a Riesz isomorphism) having the property that L(E, F) = Lr (E, F) for every Banach lattice F. Indeed, it is easy to notice that L(1'(A), F) = Lr (11 (A), F) (see for example [6, Theorem 2.1]). On the other hand, if L(E, F) = Lr(E, F) for every Banach lattice F then E is an AL-space by the result of Cartwright and Lotz. If E were not discrete then by the famous Caratheodory theorem E would contain a closed Riesz subspace Riesz isomorphic to L1 (0,1). Moreover, there exists a positive projection Received by the editors July 15, 1987 and, in revised form, August 25, 1987. 1980 Mathematics Subject Classification (1985 Revision). Primary 46B30, 47B55; Secondary 47D 15.
51 citations
TL;DR: In this article, the authors discuss some more interactions of interpolation theory with the rest of mathematics, beginning with some joint work with Coifman [CS], and their basic idea was to look for the methods of interpolations that had interesting PDE's arising as examples.
Abstract: In recent years the study of interpolation of Banach spaces has seen some unexpected interactions with other fields. (...) In this paper I shall discuss some more interactions of interpolation theory with the rest of mathematics, beginning with some joint work with Coifman [CS]. Our basic idea was to look for the methods of interpolation that had interesting PDE's arising as examples
46 citations
TL;DR: On etudie certaines equations integrodifferentielles a retard infinie dans des espaces de Banach as mentioned in this paper, i.e., certain equations integrés integrélles.
Abstract: On etudie certaines equations integrodifferentielles a retard infinie dans des espaces de Banach
45 citations
TL;DR: In this paper, it was shown that a Banach algebra A such that A ∗ has the property (V∗) of A is Arens-regular, and that the uniqueness property of the extension of the product on a unital C∗-algebra A to A∗∗ is proved.
38 citations
TL;DR: In this article, the solvability behavior on the real line of linear integrodifferential equations in a general Banach space is considered and several applications to integral partial differential equations are given.
Abstract: The solvability behavior on the real line of linear integrodifferential equations in a general Banach space is considered and several applications to integral partial differential equations are given.
TL;DR: In this article, the authors define a linear manifold Z in the given space and a norm ⦀·⦀ on Z majorizing the given norm, such that Z is a Banach space and the restriction of A to Z generates a strongly continuous semigroup of contractions in Z.
TL;DR: In this paper, the notion of general exponent of impulsive homogeneous differential equations is defined and a formula for the solution of non-homogeneous non-convex differential equations was given.
Abstract: The notion of general exponent of impulsive homogeneous differential equations is defined. A formula for the solution of impulsive nonhomogeneous differential equations is obtained and is used to establish a dependence between the existence of bounded solutions of such equations and the general exponent of the respective homogeneous equation.
01 Mar 1988
TL;DR: In this paper, a real strictly convex dual Banach space with a Frechet differentiable norm and a maximal monotone operator from E into E* such that JAx converges strongly to Px as A -A oo, where JA is the resolvent of A, and P is the nearest point mapping from E onto A-10
Abstract: Let E* be a real strictly convex dual Banach space with a Frechet differentiable norm, and A a maximal monotone operator from E into E* such that A-10 :$ 0 Fix x E E Then JAx converges strongly to Px as A -A oo, where JA is the resolvent of A, and P is the nearest point mapping from E onto A-10
Journal Article•
Book•
10 Aug 1988
TL;DR: In this article, the authors define linear ordinary differential equations, linear vector ordinary differential equation, and non-oscillation domains of differential equations with two parameters, including linear vector and linear vector ODEs.
Abstract: Scalar linear ordinary differential equations.- Linear vector ordinary differential equations.- Scalar volterra-stieltjes integral equations.- Non-oscillation domains of differential equations with two parameters.
TL;DR: In this paper, a new distance on the space of extended real-valued, lower semicontinuous convex functions defined on reflexive Banach spaces is introduced, and it is shown that the Legendre-Fenchel is an isometry.
TL;DR: In this article, the integral transformation, the Maslov canonical operator, and the asymptotics of solutions of differential equations are discussed, as well as the characteristic Cauchy problem.
Abstract: CONTENTS Introduction § 1. The integral transformation § 2. The Maslov canonical operator § 3. The asymptotics of solutions of differential equations § 4. Asymptotic solutions of the characteristic Cauchy problem References
TL;DR: In this paper, it was proved that gurantees stability under small perturbations of the general exponent of impulsive nonlinear systems in a Banach space can be guaranteed.
Abstract: A theorem is proved which gurantees stability under small perturbations of the general exponent of impulsive nonlinear systems in a Banach space.
TL;DR: The Cauchy problem in a Banach space for a non-diagonalizable limit operator was studied in this article. But it is not a generalization of the problem to the case of diagonalizable limit operators.
Abstract: CONTENTS Introduction ??1. The Cauchy problem in a Banach space for a diagonalizable limit operator ??2. The Cauchy problem in a Banach space for a non-diagonalizable limit operator Conclusion References
Journal Article•
TL;DR: In this article, the authors explore a special case of the periodic problem and prove it to be a somewhat weakened Ambrosetti-Prodi-like result, which is similar to the result in this paper.
Abstract: Abstract The aim of this paper is to explore a special case of the periodic problem and prove it to be a somewhat weakened Ambrosetti-Prodi-like result.
TL;DR: In this paper, the analytic Radon-Nikodým property for complex Banach spaces is characterized in several ways analogous to the common characterizations of the Radon Nikolaodþm property.