Showing papers in "Journal of Mathematical Analysis and Applications in 1980"

TL;DR: This paper defines the fuzzy integral of a positive, measurable function, with respect to a fuzzy measure, and shows that the monotone convergence theorem and Fatou's lemma are still true in this new setting.

TL;DR: In this paper, the Fourier transform of a function is restricted to the set cS, and the result is viewed again on cS. The operator in (1) consists of restricting $k(~) to cS and in (2) restricting the transform of the function so obtained to c S, and viewing the result again oncS.

TL;DR: In this paper, a theory of neighborhood structures and theorems in the theory of Moore-Smith's convergence are generalized to fuzzy topological spaces, including product spaces and quotient spaces.

TL;DR: Appert and Fan as mentioned in this paper showed that every upper semicontinuous L-fuzzy subset of a generalized topological space can be represented by a τ-closed random set.

TL;DR: In this article, the authors studied the dependence of Z (a, r) on a, r, where each aj is a nonzero real number and r is an n-vector, and gave information about the preservation of stability with respect to variations in the delays.

TL;DR: The existence of positive solutions of elliptic eigenvalue problems of the form (0.1) has been investigated extensively in recent years; see as discussed by the authors for a survey article.

TL;DR: In this paper, Brouwer's fixed-point theorem and Hall's theorem on systems of distinct representatives were used to prove that the piece of cake assigned to each representative is at least as large (in his own measure) as that assigned to anyone else.

TL;DR: Theorem 3.3 as discussed by the authors establishes the existence of a positive solution of the quasilinear second order elliptic differential equation (1) below in an exterior domain in Euclidean space Rn, n 3 2.

TL;DR: In this article, the motion of a vibrating string constrained to remain above a material concave obstacle is studied, and it is assumed that the string does not lose energy when it hits the obstacle; an energy condition in an ad hoc form must be added to ensure uniqueness.

TL;DR: In this article, an initial and boundary value problem for a model equation for small-amplitude long waves is shown to be well-posed, and unique classical solutions are shown to exist, which depend continuously on variations of the specified data within appropriate function classes.

TL;DR: In this article, the Carleman linearization procedure was used to investigate the non-linear autonomous of differential equations in chemical kinetics and other fields of physics (turbulence and plasma physics).

TL;DR: In this article, conditions on the memory functions were deduced which imply that the L2 norms of such induction fields are bounded away from zero even as the damping grows in an unbounded manner.

TL;DR: In this article, the method of regularization is used to obtain least squares solutions of the linear equation Kx = y, where K is a bounded linear operator from one Hilbert space into another and the regularizing operator L is a closed densely defined linear operator.

TL;DR: In this paper, the authors considered unique continuation theorems for solution of inequalities with W allowed to be unbounded, and obtained two kinds of results: one requires W ϵ Lploc( R n) with p ⩾ n − 2 for n > 5, p > 1 3 (2n − 1) for n ⩽ 5, and another requires fW2 to be −Δ-form bounded for all f ϵ C 0∞.

TL;DR: In this paper, a function satisfying a Lipschitz property on an arbitrary set S is extended to the whole space E preserving the condition, which is obtained by performing the infimal convolution of two functions associated with the data of the problem.

TL;DR: Fokas as discussed by the authors established an isomorphism between dynamical variables of Hamilton's equations and Lie-Backlund operators of the Hamilton-Jacobi equation and obtained new cubic invariants at most cubic in the momenta.

TL;DR: In this article, a simple approach is advanced for the determination of optimal control configuration under an energy constraint, i.e., optimal locations of a limited number of controllers such that the total energy requirement for control is minimized.

TL;DR: In this paper, it was shown that Krasnosel’skii's result remains valid if (I. 1) and (1.2) are replaced by the weaker conditions -4.

TL;DR: In this article, a branching phenomenon called multiple limit point bifurcation was introduced, where two distinct smooth branches of a nonlinear functional equation intersecting in a branching fashion.

TL;DR: In this article, the existence in time and uniqueness of solutions for the Cauchy problem for the Vlasov-Maxwell system of equations in one dimension was proved and the limiting values of the field ±(x, t) as the space variable x → E ∞ were shown to be uniquely determined by the initial data.