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.

Under certain homological hypotheses on a compact 4-manifold, we prove exactness of the topological surgery sequence at the stably smoothable normal invariants. This technical result allows an extension of Cappell’s 5-dimensional splitting theorem. As an application, we analyze, up to internal s-cobordism, the splitting and fibering problems for certain 5-manifolds mapping to the circle. For ex...

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...

1 1 , , 0, , r s p u u h x u dx g x u dx x u x + + −∆ = + ∈ Ω = ∈ ∂Ω () 1, 0 p W Ω () () () 1 1 , 0. r s p u x h x u dx g x u dx in u on + +  −∆ = + Ω   = ∂Ω   () E () () 1 1 / r p s Np N p N p < < − < < − + − () () () 0 0 r h L L C ∞ ∈ Ω Ω Ω   0 1 1 1, r r p * + + = ()() 0. 1 Np r Np r N p = − + − () () 0 s g L L ∞ ∈ Ω Ω  0 1 1 1, s s p * + + = ()() 0 ,. 1 Np Np s p Np s N p N p *   ...

The moment map is a mathematical expression of the concept of the conservation associated with the symmetries of a Hamiltonian system. The abstract moment map is defined from G-manifold M to dual Lie algebra of G. We will interested study maps from G-manifold M to spaces that are more general than dual Lie algebra of G. These maps help us to reduce the dimension of a manifold much more.

In this article, we apply the Nehari manifold method to study the Kirchhoff type equation

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

In this article, we study periodic solutions of a class of delay differential equations. By restricting our discussion on generalized Nehari Manifold, some sufficient conditions are obtained to guarantee the existence of infinitely many pairs of periodic solutions. Also, there exists at least one periodic solution with prescribed minimal period.

−ε2∆u + V (x)u + ψu = f(u) in R, −ε2∆ψ = u in R, u > 0, u ∈ H(R), has been studied extensively, where the assumption for f(u) is that f(u) ∼ |u|p−2u with 4 < p < 6 and satisfies the Ambrosetti–Rabinowitz condition which forces the boundedness of any Palais– Smale sequence of the corresponding energy functional of the equation. The more difficult critical case is studied in this paper. As g(u) :...