The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator
In this paper, we study the solution of nonlinear equation Δ k B (Δ B + m 2 ) k u(x) = f(x,Δ k-1 B (Δ B + m 2 ) k u(x)) where the operator Δ k B is the Bessel Laplace operator iterated k-times defined by Δ k B = (B x1 + B x2 + · · · + B xn ) k n is the dimension of the space R + n , x = (x...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Journal |
| Published: |
2017
|
| Online Access: | https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77953900558&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43279 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Institution: | Chiang Mai University |
| id |
th-cmuir.6653943832-43279 |
|---|---|
| record_format |
dspace |
| spelling |
th-cmuir.6653943832-432792017-09-28T06:53:30Z The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator Niyom S. Kananthai A. In this paper, we study the solution of nonlinear equation Δ k B (Δ B + m 2 ) k u(x) = f(x,Δ k-1 B (Δ B + m 2 ) k u(x)) where the operator Δ k B is the Bessel Laplace operator iterated k-times defined by Δ k B = (B x1 + B x2 + · · · + B xn ) k n is the dimension of the space R + n , x = (x 1 , x 2 ,..., x n ) E R + n , k is a positive integer, u(x) is an unknown and f is a given function. It is found that the existence of the solution u(x) of such equation depending on the condition of f and Δ k-1 B (Δ B +m 2 ) k u(x). Moreover such solution u(x) related to the nonhomogeneous Bessel biharmonic equation depend on the conditions of k. 2017-09-28T06:53:30Z 2017-09-28T06:53:30Z 2010-06-29 Journal 2-s2.0-77953900558 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77953900558&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43279 |
| institution |
Chiang Mai University |
| building |
Chiang Mai University Library |
| country |
Thailand |
| collection |
CMU Intellectual Repository |
| description |
In this paper, we study the solution of nonlinear equation Δ k B (Δ B + m 2 ) k u(x) = f(x,Δ k-1 B (Δ B + m 2 ) k u(x)) where the operator Δ k B is the Bessel Laplace operator iterated k-times defined by Δ k B = (B x1 + B x2 + · · · + B xn ) k n is the dimension of the space R + n , x = (x 1 , x 2 ,..., x n ) E R + n , k is a positive integer, u(x) is an unknown and f is a given function. It is found that the existence of the solution u(x) of such equation depending on the condition of f and Δ k-1 B (Δ B +m 2 ) k u(x). Moreover such solution u(x) related to the nonhomogeneous Bessel biharmonic equation depend on the conditions of k. |
| format |
Journal |
| author |
Niyom S. Kananthai A. |
| spellingShingle |
Niyom S. Kananthai A. The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
| author_facet |
Niyom S. Kananthai A. |
| author_sort |
Niyom S. |
| title |
The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
| title_short |
The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
| title_full |
The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
| title_fullStr |
The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
| title_full_unstemmed |
The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
| title_sort |
nonlinear product of the bessel laplace operator and the bessel helmholtz operator |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77953900558&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43279 |
| _version_ |
1681422348147752960 |