On the nonlinear product of Laplacian related to the biharmonic equation
In this paper, we study the solution of nonlinear equation of the form, where the operator Δ k is the Laplacian defined by, n is the dimension of the Euclidean space R{double-struck} n , x = (x 1 , x 2 ,..., x n ) ε R{double-struck} 0 , k is a positive integer, u(x) is an unknown and f is a given f...
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th-cmuir.6653943832-431652017-09-28T06:51:18Z On the nonlinear product of Laplacian related to the biharmonic equation Panyatip T. Kananthai A. In this paper, we study the solution of nonlinear equation of the form, where the operator Δ k is the Laplacian defined by, n is the dimension of the Euclidean space R{double-struck} n , x = (x 1 , x 2 ,..., x n ) ε R{double-struck} 0 , 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 (Δ+m 2 ) k u(x) and moreover such solution u(x) related to the Laplacian depending on the conditions of k. 2017-09-28T06:51:18Z 2017-09-28T06:51:18Z 2010-12-01 Journal 13128876 2-s2.0-79251642263 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79251642263&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43165 |
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Chiang Mai University Library |
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Thailand |
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In this paper, we study the solution of nonlinear equation of the form, where the operator Δ k is the Laplacian defined by, n is the dimension of the Euclidean space R{double-struck} n , x = (x 1 , x 2 ,..., x n ) ε R{double-struck} 0 , 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 (Δ+m 2 ) k u(x) and moreover such solution u(x) related to the Laplacian depending on the conditions of k. |
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Journal |
| author |
Panyatip T. Kananthai A. |
| spellingShingle |
Panyatip T. Kananthai A. On the nonlinear product of Laplacian related to the biharmonic equation |
| author_facet |
Panyatip T. Kananthai A. |
| author_sort |
Panyatip T. |
| title |
On the nonlinear product of Laplacian related to the biharmonic equation |
| title_short |
On the nonlinear product of Laplacian related to the biharmonic equation |
| title_full |
On the nonlinear product of Laplacian related to the biharmonic equation |
| title_fullStr |
On the nonlinear product of Laplacian related to the biharmonic equation |
| title_full_unstemmed |
On the nonlinear product of Laplacian related to the biharmonic equation |
| title_sort |
on the nonlinear product of laplacian related to the biharmonic equation |
| publishDate |
2017 |
| url |
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=79251642263&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43165 |
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1681422326925623296 |