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Open Access Green as soon as Postprint is submitted to ZB.
Solvability in the sense of sequences for some linear and nonlinear Fredholm operators with the logarithmic Laplacian.
Complex Variables, DOI: 10.1080/17476933.2023.2293796 (2024)
We study the solvability of certain linear and nonlinear nonhomogeneous equations in one dimension involving the logarithmic Laplacian and the transport term. In the linear case we show that the convergence in (Formula presented.) of their right sides yields the existence and the convergence in (Formula presented.) of the solutions. We generalize the results obtained in the earlier article of Efendiev and Vougalter [Solvability in the sense of sequences for some non-Fredholm operators with the logarithmic Laplacian. Monatsh Math. 2023] in the non-Fredholm case without the drift. In the nonlinear part of the work we demonstrate that, under the reasonable technical assumptions, the convergence in (Formula presented.) of the integral kernels implies the existence and the convergence in (Formula presented.) of the solutions.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Fredholm Operators ; Integral Kernel ; Logarithmic Laplacian ; Solvability Conditions; Properness Properties; Elliptic-operators; Traveling-waves; Holder Theory; Dirichlet; Equations; Systems
ISSN (print) / ISBN
0278-1077
e-ISSN
1563-5066
Publisher
Taylor & Francis
Publishing Place
2-4 Park Square, Milton Park, Abingdon Or14 4rn, Oxon, England
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)
Grants
NSERC