Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

We will prove a Moser-type theorem for self-dual harmonic 2-forms on closed 4manifolds, and use it to classify local forms on neighborhoods of singular circles on which the 2-form vanishes. Removing neighborhoods of the circles, we obtain a symplectic manifold with contact boundary we show that the contact form on each S1×S2, after a slight modification, must be one of two possibilities.

We define integrable, big-isotropic structures on a manifold M as subbundles E ⊆ T M ⊕ T * M that are isotropic with respect to the natural, neutral metric (pairing) g of T M ⊕ T * M and are closed by Courant brackets (this also implies that [E, E ⊥g ] ⊆ E ⊥g). We give the interpretation of such a structure by objects of M , we discuss the local geometry of the structure and we give a reduction...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the center of such...

In smooth manifold theory, the notion of a tangent space makes it possible for differentiation to take place on an abstract manifold. In this paper, the notion of a distribution will be presented which makes it possible for integration to take place on an abstract manifold. The first section introduces terminology and builds intuition via an analogy to the concept of integral curves. The second...

Using a nonlocal version of the center-manifold theorem and normal form reduction, we prove existence small-amplitude generalized solitary-wave solutions modulated to steady gravity-capillary Whitham equation with weak surface tension. Through application theorem, for solitary wave profiles is reduced four-dimensional system ODEs inheriting reversibility. Along particular parameter curves, rela...

Abstract In this paper, a discrete Leslie-Gower predator-prey system with Michaelis-Menten type harvesting is studied. Conditions on the existence and stability of fixed points are obtained. It shown that can undergo fold bifurcation, flip Neimark-Sacker bifurcation by using center manifold theorem theory. Numerical simulations presented to illustrate main theoretical results. Compared continuo...

A direct, bundle-theoretic method for defining and extending local isometries out of curvature data is developed. As a by-product, conceptual direct proofs of a classical result of Singer and a recent result of the authors are derived. A classical result of I. M. Singer [7] states that a Riemannian manifold is locally homogeneous if and only if its Riemannian curvature tensor together with its ...

We study a class of asymptotically cylindrical Ricci-flat Kähler metrics arising on quasiprojective manifolds. Using the Calabi–Yau geometry and analysis and the Kodaira–Kuranishi–Spencer theory and building up on results of N.Koiso, we show that under rather general hypotheses any local asymptotically cylindrical Ricci-flat deformations of such metrics are again Kähler, possibly with respect t...