World Scientific
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.
Communications in Contemporary Mathematics cover
Submit an article Subscribe
About the Journal

Volume 10, Issue 03 (June 2008)

No Access
ASYMPTOTIC CURVES ON SURFACES IN ℝ5
  • Pages:309–335

https://doi.org/10.1142/S0219199708002806

Preview Abstract

We study asymptotic curves on generically immersed surfaces in ℝ5. We characterize asymptotic directions via the contact of the surface with flat objects (k-planes, k = 1 - 4), give the equation of the asymptotic curves in terms of the coefficients of the second fundamental form and study their generic local configurations.

No Access
EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH A GENERAL INDEFINITE WEIGHT
  • Pages:337–362

https://doi.org/10.1142/S021919970800279X

Preview Abstract

This paper studies the existence of positive solutions for a class of singular boundary value problems of p-Laplacian. By using Global Continuation Theorem and the fixed point index technique, criteria of the existence, multiplicity and nonexistence of positive solutions are established.

No Access
PROJECTIVE ℚ-FACTORIAL TORIC VARIETIES COVERED BY LINES
  • Pages:363–389

https://doi.org/10.1142/S0219199708002818

Preview Abstract

We give a structural theorem for ℚ-factorial toric varieties covered by lines in ℙN, and compute their dual defect. This yields a characterization of defective ℚ-factorial toric varieties in ℙN. The combinatorial description of such varieties is used to characterize some finite sets of monomials with discriminant equal to one.

No Access
MULTIPLE BOUND STATES FOR THE SCHRÖDINGER–POISSON PROBLEM
  • Pages:391–404

https://doi.org/10.1142/S021919970800282X

Preview Abstract

In this paper, we study the problem

formula
where u, V : ℝ3 → ℝ are radial functions, λ > 0 and 1 < p < 5. We give multiplicity results, depending on p and on the parameter λ.

No Access
ON THE UNIQUENESS OF POSITIVE SOLUTIONS OF A QUASILINEAR EQUATION CONTAINING A WEIGHTED p-LAPLACIAN, THE SUPERLINEAR CASE
  • Pages:405–432

https://doi.org/10.1142/S0219199708002831

Preview Abstract

We consider the quasilinear equation of the form

formula
where Δpu ≔ div(|∇u|p-2∇u) is the degenerate p-Laplace operator and the weight K is a positive C1 function defined in ℝ+. We deal with the case in which f ∈ C[0,∞) has one zero at u0 > 0, is non positive and not identically 0 in (0,u0), and is locally Lipschitz, positive and satisfies some superlinear growth assumption in (u0,∞). We carefully study the behavior of the solution of the corresponding initial value problem for the radial version of the quasilinear equation, as well as the behavior of its derivative with respect to the initial value. Combining, as Cortázar, Felmer and Elgueta, comparison arguments due to Coffman and Kwong, with some separation results, we show that any zero of the solutions of the initial value problem is monotone decreasing with respect to the initial value, which leads immediately the uniqueness of positive radial ground states, and the uniqueness of positive radial solutions of the Dirichlet problem on a ball.

No Access
EQUIVARIANT COHOMOLOGY AND HOLOMORPHIC INVARIANT
  • Pages:433–447

https://doi.org/10.1142/S0219199708002843

Preview Abstract

Using equivariant cohomology, we construct a family of holomorphic invariants which include the famous Futaki invariant and its generalization to singular variety as special cases. We are also using this viewpoint to compute the generalized Futaki invariant for complete intersections.

No Access
FINITE SPECIAL MOUFANG SETS OF EVEN CHARACTERISTIC
  • Pages:449–454

https://doi.org/10.1142/S0219199708002855

Preview Abstract

We give a short and elementary proof of the fact that a finite special Moufang set with root groups of even order is isomorphic to the unique Moufang set whose little projective group is PSL2(2k) for some integer k ≥ 1.

No Access
FINITE SPECIAL MOUFANG SETS OF ODD CHARACTERISTIC
  • Pages:455–475

https://doi.org/10.1142/S0219199708002867

Preview Abstract

In this paper we classify finite special Moufang sets 𝕄(U,τ) of odd characteristic. The characteristic 2 case was handled in another paper by De Medts and the author (see [3]). We prove that U is elementary abelian. Then, we show that 𝕄(U,τ) is the unique Moufang set whose little projective group is PSL2(|U|). The emphasis of this paper is on obtaining elementary proofs. Section 3 deals with root subgroups in any Moufang set and may be of independent interest.

Previous
Next