Class Of Operator Equations Research Articles

Nonlinear integral operators and chaos in Banach spaces

Sufficient conditions are given for chaotic behaviour of continuous transformations on Banach spaces. The conditions avoid the requirement that mappings be expanding on compact sets and are probably easier to verify for many classes of operator equations than existing criteria. Two classes of integral operators on C[0, 1] are considered in the light of these results: one nonlinear but compact, the second noncompact.

Role of determinism in query languages for data bases

7. V. P. Podporin, "Solutions of the operator equation PI(D)A = AP2(D) in certain classes of linear operators," Dokl. Akad. Nauk SSSR, 240, 28 (1978). V. P. Zakharyuta and M. Yu. Tsar'kov, "Operators that commute with multiplication in analytic one-variable function spaces," Mat. Zametki, 13, 269 (1973). N. E. Linchuk and S. S. Linchuk, "A class of operator equations in analytic spaces," Ukr. Mat. Zh., 35, 510 (1983).

A class of operator equations in analytic spaces

A class of operator equations in analytic spaces

A Class of Operator Equations in Nonlinear Mechanics

A nonlinear evolution equation in Hilbert space is introduced and is shown to govern a broad class of problems of nonlinear solid mechanics. The simplest oscillations of this equation are described by a “generalized Lienard equation.” AMS(MOS) Classification Nos: 73D35, 73F15, 58D25, 35L35, 34G20, 34C15.

Approximate solution of a class of operator equations

Approximate solution of a class of operator equations

An iterative method directly applicable to differential equations

A study of a class of operator equations with unbounded operator by methods of theory of weighted approximation of functions provides a basis for an explicit iterative method, applicable to the case of a self-adjoint positive definite second-order differential operator with analytic coefficients.

Multiparametered nonhomogeneous nonlinear equations

where X is a real parameter, z is a fixed element of a Banach space, and the nonlinear operator F satisfies certain positivity conditions. For the special nonhomogeneous case with z = 0, but FQ, 0) # 0, W. R. Derrick and H. J. Kuiper [2] have shown the existence of an unbounded continuum of positive solutions (A, w). The first result extends their theorem to equation (1) and to an analogous multiparametered equation. Similar results for the homogeneous equation have been obtained by M. A. KrasnosePskii [4], P. H. Rabinowitz [6], R. E. L. Turner [8] and others, in the single-parametered case; and by J. C. Alexander and J. A. Yorke [1] in the multiparametered case. The second class of operator equations is given by the equation u -fF(u) = w; where w is a fixed member of a Banach space. Assuming that ||F(w)|| g a|| i/1|, 0 where Xtis a real parameter and ztis a fixed member of the Banach space for 1 g / ^ «. To illustrate possible applications of these results, we consider two problems in nonlinear elasticity. The first problem is the motion of an inelastic string with one endpoint free. Under the assumption that the string is acted on solely by forces of gravity and tension, this problem has been considered by I. I. Kolodner [3], using classical analysis, C. A. Stuart [6], using operator theory, and others. We consider the case that the string is also acted on by an external force and show the existence of

Generic Properties for Some Classes of Operator Equations

Generic Properties for Some Classes of Operator Equations

Approximation von operatorgleichungen mit reprokernen

In this paper we develop a method for the approximation of a broad class of operator equations by reproducing kernels. The relevant operators are defined on Hilbert spaces. Necessary and sufficient conditions for the convergence of the approximation are discussed in detail. The results can be applied-for example-to Fredholm integral operators of the first and second kind and to ordinary and partial differential operators of elliptic type. In this context we refer to [9] for methods to construct reproducing kernels.

One class of operator equations of the first kind

One class of operator equations of the first kind

A class of operator equations of the first kind

A class of operator equations of the first kind

On a certain class of operator equations

On a certain class of operator equations