In this paper, we give a characterization of the finite multiplicity of a CR mapping between real analytic hypersurfaces. The finite multiplicity of a CR mapping was defined algebraically by Baouendi and Rothschild in [BR1] (see the definition below). We will prove that under certain conditions on hypersurfaces the finite multiplicity of a CR mapping is equivalent to that the preimage of the ma...

Using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of Monge-Amp`{e}re equations are established‎.‎

This article is devoted to the study of existence and multiplicity of positive solutions to a class of nonlinear fractional order multi-point boundary value problems of the type−Dq0+u(t) = f(t, u(t)), 1 < q ≤ 2, 0 < t < 1,u(0) = 0, u(1) =m−2∑ i=1δiu(ηi),where Dq0+ represents standard Riemann-Liouville fractional derivative, δi, ηi ∈ (0, 1) withm−2∑i=1δiηi q−1 < 1, and f : [0, 1] × [0, ∞) → [0, ...

where the A{ are rational integers, is called an integral linear recurrence of order k. Given such a linear recurrence and an integer c, one would like to know for what n does f(n) — c? In a very few particular instances (e.g. see [2], [6]) this question has been answered, but in general the question is very difficult. A less exacting problem is the determination of upper and lower bounds on th...

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

If φ is an analytic map of the unit diskD into itself, the composition operator Cφ on the Hardy space H (D) is defined by Cφ(f) = f ◦ φ. For a certain class of composition operators with multivalent symbol φ, we identify a subspace of H(D) on which C∗ φ behaves like a weighted shift. We reproduce the description of the spectrum found in [5] and show for this class of composition operators that ...

We consider the local Ginzburg-Rallis model over complex field. We show that the multiplicity is always 1 for a majority of the generic representations. We also have partial results on the real case for general generic representations. This is a sequel work of [Wan15] and [Wan16] on which we considered the p-adic case and the real case for tempered representations.

Let A be a commutative unital C-algebra and let  denote its Gelfand spectrum. We find some necessary and sufficient conditions for a nondegenerate representation of A to be unitarily equivalent to a multiplicative representation on a space L(Â, μ), where μ is a positive measure on the Baire sets of Â. We also compare these conditions with the multiplicity-free property of a representation.