Results 11 to 20 of about 12,976 (302)

Existence of nontrivial solutions for semilinear problems with strictly differentiable nonlinearity [PDF]

Abstract and Applied Analysis, 2006
The existence of a nontrivial solution for semilinear elliptic problems with strictly differentiable nonlinearity is proved. A result of homological linking under nonstandard geometrical assumption is also shown. Techniques of Morse theory are employed.
Sergio Lancelotti
doaj   +3 more sources

Prescribing Morse Scalar Curvatures: Pinching and Morse Theory [PDF]

Communications on Pure and Applied Mathematics, 2021
AbstractWe consider the problem of prescribing conformally the scalar curvature on compact manifolds of positive Yamabe class in dimension . We prove new existence results using Morse theory and some analysis on blowing‐up solutions under suitable pinching conditions on the curvature function.
Malchiodi, Andrea, Mayer, Martin
openaire   +5 more sources

Multiparameter discrete Morse theory

Journal of Applied and Computational Topology
The main objective of this paper is to extend Morse-Forman theory to vector-valued functions. This is mostly motivated by the need to develop new tools and methods to compute multiparameter persistence. To generalize the theory, in addition to adapting the main definitions and results of Forman to this vectorial setting, we use concepts of ...
Guillaume Brouillette, Madjid Allili, Tomasz Kaczynski   +2 more
openaire   +3 more sources

Discrete microlocal Morse theory

Journal of Pure and Applied Algebra
We establish several results combining discrete Morse theory and microlocal sheaf theory in the setting of finite posets and simplicial complexes. Our primary tool is a computationally tractable description of the bounded derived category of sheaves on a poset with the Alexandrov topology. We prove that each bounded complex of sheaves on a finite poset
Adam Brown, Ondřej Draganov
core   +4 more sources

Multiple Periodic Solutions to Nonlinear Discrete Hamiltonian Systems

Advances in Difference Equations, 2007
An existence result of multiple periodic solutions to the asymptotically linear discrete Hamiltonian systems is obtained by using the Morse index theory.
Bo Zheng
doaj   +2 more sources

Morse theory for C*-algebras: a geometric interpretation of some noncommutative manifolds

Applied General Topology, 2011
The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. Some examples are given to illustrate these geometric information.
Vida Milani, Ali Asghar Rezaei, Seyed M.H. Mansourbeigi   +2 more
doaj   +1 more source

Research on P System with Chain Structure and Application and Simulation in Arithmetic Operation

Discrete Dynamics in Nature and Society, 2015
Considering the advantages of distribution and maximum parallelism of membrane computing and availability of discrete Morse theory to deal with discrete structure, in this paper, combining discrete Morse theory and membrane computing, a novel membrane ...
Jing Luan, Zhong Yao
doaj   +1 more source

Multiple Solutions for Biharmonic Equations with Asymptotically Linear Nonlinearities

Boundary Value Problems, 2010
The existence of multiple solutions for a class of fourth elliptic equation with respect to the resonance and nonresonance conditions is established by using the minimax method and Morse theory.
Ruichang Pei
doaj   +2 more sources

Multi-dimensional Morse Index Theorems and a symplectic view of elliptic boundary value problems [PDF]

, 2011
Morse Index Theorems for elliptic boundary value problems in multi-dimensions are proved under various boundary conditions. The theorems work for star-shaped domains and are based on a new idea of measuring the "oscillation" of the trace of the set of ...
Deng, Jian, Jones, C. K. R. T. (Christopher K. R. T.)   +1 more
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Existence and Multiplicity of Solutions for Discrete Nonlinear Two-Point Boundary Value Problems

Discrete Dynamics in Nature and Society, 2011
By using Morse theory, the critical point theory, and the character of 𝐾1/2, we consider the existence and multiplicity results of solutions to the following discrete nonlinear two-point boundary value problem −Δ2𝑥(𝑘−1)=𝑓(𝑘,𝑥(𝑘)),𝑘∈ℤ(1,𝑇) subject to 𝑥(0)=
Jianmin Guo, Caixia Guo
doaj   +1 more source