A Montgomery-Samelson (MS) fibering is a fibering with singularities such that the singular fibers are points. A fiber map is a map that preserves fibers and takes singular fibers to singular fibers. For MS fiberings that are the suspension of a map of a space to a point, and hence the base space is an interval, we obtain a formula for the minimum number of fixed points among all fiber maps tha...

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎. 

‎by considering a degenerate $p(x)-$laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent sobolev space is presented‎. ‎multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding nehari manifold‎.

The quantum modular invariant jqt(θ) of θ ∈R is defined as a discontinuous PGL2(Z)-invariant multi-valued map using the distance-to-the-nearest-integer function ‖ · ‖. For θ ∈Q it is shown that jqt(θ) =∞ and for quadratic irrationalities PARI/GP experiments suggest that jqt(θ) is a finite set. In the case of the golden mean φ, we produce explicit formulas involving weighted versions of the Roge...

In a recent paper [2], Montgomery and Samelson have raised the question whether there exists, for some n, a compact fibering of Euclidean w-space, and have given some reasons for thinking that no such fibering is possible. The purpose of this note is to provide further evidence for this belief by proving that a t least there is no compact fibering of the plane. The theorem I shall prove is in f...

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.

We prove two kinds of fibering theorems for maps X → P , where X and P are Poincaré spaces. The special case of P = S1 yields a Poincaré duality analogue of the fibering theorem of Browder and Levine.

this study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. our results is depending onthe local minimization method on the nehari manifold and some variational techniques. alsoby using mountain pass lemma, we establish the existence of at least one solution withpositive energy.

We consider the semilinear elliptic system { −∆u+m1(x)u = fu(x, u, v) x ∈ Ω, −∆v +m2(x)v = fv(x, u, v) x ∈ Ω, with the boundary conditions ∂u ∂n = λg(x, u) and ∂v ∂n = μh(x, v), where Ω ⊂ RN is a bounded smooth domain, λ, μ > 0 and the functions f , g, h, m1 and m2 satisfy some suitable conditions. Using the fibering map and by extracting the Palais-Smale sequences in the Nehari manifold, we pr...

We prove the existence of at least two positive solutions for the semilinear elliptic boundary-value problem −∆u(x) = λa(x)u + b(x)u for x ∈ Ω; u(x) = 0 for x ∈ ∂Ω on a bounded region Ω by using the Nehari manifold and the fibering maps associated with the Euler functional for the problem. We show how knowledge of the fibering maps for the problem leads to very easy existence proofs.