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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| Main Authors: | , |
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| Format: | Journal |
| Published: |
2017
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| Online Access: | 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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| Institution: | Chiang Mai University |
| Summary: | 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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