Abstract
In this paper, we provide an affirmative response to the following question: if Morse-Novikov cohomology groups of M with non-empty boundary ∂M do not vanish, then what topological or analytical(geometrical) constraints can be enforced to ensure that the equation 𝖽θω=η is solvable for any non-trivialprescribed [η] in absolute Hθk(M) or relative Hθk(M,∂M) Morse-Novikov cohomology groups?. Where 𝖽θω=𝖽ω+θ∧ω and 0≠[θ]∈HdR1(M) for any ω∈Ωk(M). Moreover, this motivates us to investigate the integrability requirements for a variety of perturbed Dirichlet problems for 𝖽θ, Neumann problems for δθ, and perturbed mixed boundary value problems for the Poisson equation from topological and analytical perspectives. Furthermore, we investigate the analytical properties of the eigenvalues of the spacial kind of Poisson equations and show that they are positive and their corresponding eigenfunctions are L2-orthogonal. Consequently, this proves that the set of the corresponding eigenfunctions spans a subspace of the orthogonal complement of the kernel of this equation.
Recommended Citation
Al-Zamil, Qusay S. A. and Abass, Mohammed Y.
(2025)
"Boundary Value Problems Associated with Morse-Novikov Cohomology Groups of Riemannian Manifolds with Boundary,"
Iraqi Journal for Computer Science and Mathematics: Vol. 6:
Iss.
2, Article 25.
DOI: https://doi.org/10.52866/2788-7421.1266
Available at:
https://ijcsm.researchcommons.org/ijcsm/vol6/iss2/25
