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Solvability in the sense of sequences for some fourth order non-Fredholm operators.
J. Differ. Equations 271, 280-300 (2021)
We study solvability of some linear nonhomogeneous elliptic problems and establish that under reasonable technical conditions the convergence in L2(Rd) of their right sides implies the existence and the convergence in H4(Rd) of the solutions. The problems contain the squares of the sums of second order non-Fredholm differential operators and we use the methods of the spectral and scattering theory for Schrödinger type operators. We especially emphasize that here we deal with the fourth order operators in contrast to the second order operators in [29] and investigate the dependence of the solvability conditions on the dimension of our problem when the constant a=0. We also consider the case of solvability with a single potential in an arbitrary dimension.
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Publication type
Article: Journal article
Document type
Scientific Article
Keywords
Non-fredholm Operators ; Sobolev Spaces ; Solvability Conditions
ISSN (print) / ISBN
0022-0396
e-ISSN
1090-2732
Quellenangaben
Volume: 271,
Pages: 280-300
Publisher
Elsevier
Publishing Place
525 B St, Ste 1900, San Diego, Ca 92101-4495 Usa
Non-patent literature
Publications
Reviewing status
Peer reviewed
Institute(s)
Institute of Computational Biology (ICB)
Grants
NSERC