Solvability in the sense of sequences to some non-Fredholm operators
We study the solvability of certain linear nonhomogeneous elliptic problems and show that under reasonable technical conditions the convergence in $L^2(mathbb{R}^d)$ of their right sides implies the existence and the convergence in $H^2(mathbb{R}^d)$ of the solutions. The equations involve secon...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-07-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/160/abstr.html |
| _version_ | 1818917551754706944 |
|---|---|
| author | Vitaly Volpert Vitali Vougalter |
| author_facet | Vitaly Volpert Vitali Vougalter |
| author_sort | Vitaly Volpert |
| collection | DOAJ |
| description | We study the solvability of certain linear nonhomogeneous elliptic problems and show that under reasonable technical conditions the convergence in $L^2(mathbb{R}^d)$ of their right sides implies the existence and the convergence in $H^2(mathbb{R}^d)$ of the solutions. The equations involve second order differential operators without Fredholm property and we use the methods of spectral and scattering theory for Schrodinger type operators analogously to our preceding work [17]. |
| first_indexed | 2024-12-20T00:35:52Z |
| format | Article |
| id | doaj.art-5def22ac4b0547e48cf30848773d3928 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-20T00:35:52Z |
| publishDate | 2013-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-5def22ac4b0547e48cf30848773d39282022-12-21T19:59:45ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-07-012013160,116Solvability in the sense of sequences to some non-Fredholm operatorsVitaly VolpertVitali VougalterWe study the solvability of certain linear nonhomogeneous elliptic problems and show that under reasonable technical conditions the convergence in $L^2(mathbb{R}^d)$ of their right sides implies the existence and the convergence in $H^2(mathbb{R}^d)$ of the solutions. The equations involve second order differential operators without Fredholm property and we use the methods of spectral and scattering theory for Schrodinger type operators analogously to our preceding work [17].http://ejde.math.txstate.edu/Volumes/2013/160/abstr.htmlSolvability conditionsnon Fredholm operatorsSobolev spaces |
| spellingShingle | Vitaly Volpert Vitali Vougalter Solvability in the sense of sequences to some non-Fredholm operators Electronic Journal of Differential Equations Solvability conditions non Fredholm operators Sobolev spaces |
| title | Solvability in the sense of sequences to some non-Fredholm operators |
| title_full | Solvability in the sense of sequences to some non-Fredholm operators |
| title_fullStr | Solvability in the sense of sequences to some non-Fredholm operators |
| title_full_unstemmed | Solvability in the sense of sequences to some non-Fredholm operators |
| title_short | Solvability in the sense of sequences to some non-Fredholm operators |
| title_sort | solvability in the sense of sequences to some non fredholm operators |
| topic | Solvability conditions non Fredholm operators Sobolev spaces |
| url | http://ejde.math.txstate.edu/Volumes/2013/160/abstr.html |
| work_keys_str_mv | AT vitalyvolpert solvabilityinthesenseofsequencestosomenonfredholmoperators AT vitalivougalter solvabilityinthesenseofsequencestosomenonfredholmoperators |