Showing papers on "C0-semigroup published in 1979"

Topological degree methods in nonlinear boundary value problems

Abstract: Introduction Suggestions for the readerSuggestions for the reader Fredholm mappings of index zero and linear boundary value problems Degree theory for some classes of mappings Duality theorems for several fixed point operators associated to periodic problems for ordinary differential equations Existence theorems for equations in normed spaces Boundary value problems for second order nonlinear vector differential equations Periodic solutions of ordinary differential equations with one-sided growth restrictions Bound sets for functional differential equations The index of isolated zeros of some mappings Bifurcation theory Periodic solutions of autonomous ordinary differential equations around an equilibrium References.

Multiple positive fixed points of nonlinear operators on ordered Banach spaces

Abstract: The existence of multiple positive fixed points of completely continuous nonlinear operators defined on the cone of an ordered Banach space is considered. The main results give sufficient conditions for such an operator to have two, and in some cases three, positive fixed points. (RWR)

Strong convergence of contraction semigroups and of iterative methods for accretive operators in Banach spaces

Abstract: LetA be anm-accretive operator in a Banach spaceE. Suppose thatA −10 is not empty and that bothE andE * are uniformly convex. We study a general condition onA that guarantees the strong convergence of the semigroup generated by—A and of related implicit and explicit iterative schemes to a zero ofA. Rates of convergence are also obtained. In Hilbert space this condition has been recently introduced by A. Pazy. We also establish strong convergence under the assumption that the interior ofA −10 is not empty. In Hilbert space this result is due to H. Brezis.

Nonlinear boundary value problems in Banach spaces for multivalue differential equations on a non-compact interval

Abstract: where A and L are linear operators and M is a continuous, generally nonlinear operator. We want to show that, under suitable hypotheses, the problem (1.1) has a solution defined on an interval J = [a, b), x < a < b d + xc;. The analogous problem for ordinary differential equations on a compact interval has been treated by Scrucca [ 11. The linear boundary value problem has been studied by Cecchi et al. [Z] in the univoque case and by Anichini and Zecca [3,4], in the multivoque one. For a wide bibliography and exposition on boundary value problems for differential equations see Conti [5]. 2. NOTATIONS AND HYPOTHESES

Best approximation and intersections of balls in Banach spaces

Abstract: Let E be a Banach space, M a closed subspace of E with the 3-ball property. It is known that M is proximinal in E , and that its metric projection admits a continuous selection. This means that there is a continuous (generally non-linear) map π: E → M satisfying ‖ x −π( x )‖ = d ( x , M ) for all x in E . Here it is shown that the same conclusion holds under a much weaker hypothesis on M , which we call the 1½-ball property. We also establish that if M has the 1½-ball property in E , then there is a continuous Hahn-Banach extension map from M * to E *.

Banach lattices - some banach aspects of their theory

Abstract: CONTENTSIntroduction § 1. Preliminary results from the theory of Banach lattices § 2. Banach invariant properties of Banach lattices § 3. Banach invariant properties and Banach constants in Banach lattices § 4. Banach theorems in the theory of Banach lattices § 5. The approximation problem in Banach lattices § 6. On Banach spaces that are isomorphic or isometric to Banach lattices, and Banach spaces with local unconditional structureGuide to the literatureReferences

Compactness principles in nonlinear operator approximation theory

Abstract: This paper is concerned with the approximate solution of nonlinear operator equations in abstract settings and with applications to integral and differential equations. A given operator with certain continuity and compactness or inverse compactness properties is a suitable limit of a sequence of operators with analogous properties which hold uniformly or asymptotically. Both fixed point equations and inhomogeneous equations are treated. Solutions of approximate problems converge to solutions of the given problem. This is an appropriate type of set convergence when solutions are not unique.

Banach Convolution Algebras of Functions II.

Abstract: LetG be a noncompact, locally compact group. By means of “generalized dyadic decompositions” ofG, translation invariant Banach spacesF(B, B, X) of (classes of) measurable functions onG are constructed, e. g. certain weighted amalgams ofLp-spaces. Basic properties of these spaces are derived and connections with spaces considered in the literature are indicated. As a main result, sufficient conditions are given which imply that a space of this type is a Banach algebra with respect to convolution.

Convexity, boundedness,andalmost periodicity for differential equations in hilbertspace

Abstract: There are three kinds of results. First we extend and sharpen a convexity inequality of Agmon and Nirenberg for certain differential inequalities in Hilbert space. Next we characterize the bounded solutions of a differential equation in Hilbert space involving and arbitrary unbounded normal operator. Finally, we give a general sufficient condition for a bounded solution of a differential equation in Hilbert space to be almost

Remarks on generators of analytic semigroups

Abstract: This paper contains two new characterizations of generators of analytic semigroups of linear operators in a Banach space. These characterizations do not require use of complex numbers. One is used to give a new proof that strongly elliptic second order partial differential operators generate analytic semigroups inL p , 1

The Poincaré–Bendixson theorem for certain differential equations of higher order

Abstract: By adapting its well-known proof, the Poincare–Bendixson theorem, on the existence of periodic orbits of plane autonomous systems, is extended to vector differential equations of the form f(D)x + bφ(g(D)x) = 0. The only restrictions placed on the vector function φ(y) are that its Jacobian matrix should be continuous and lie within a suitably chosen ellintic ball.

Solvability and properties of solutions of nonlinear elliptic equations

Abstract: The paper contains an exposition of variational and topological methods of investigating general nonlinear operator equations in Banach spaces. Application is given of these methods to the proof of solvability of boundary-value problems for nonlinear elliptic equations of arbitrary order, to the problem of eigenfunctions, and to bifurcation of solutions of differential equations. Results are presented of investigations of the properties of generalized solutions of quasilinear elliptic equations of higher order.

On the existence of solutions to coupled matrix Riccati differential equations in linear quadratic Nash games

Abstract: Sufficient conditions for the existence of closed-loop linear Nash strategies for a linear quadratic game are derived through use of diffrential inequalities.

A remarkable homogeneous Banach algebra

Abstract: We give an example of a strongly homogeneous Banach algebraB withA(T)⊊B⊊C(T) on which all 1-Lipschitzian functions operate; this improves previous results of M. Zafran.