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...
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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=77953900558&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/43279 |
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| Institution: | Chiang Mai University |
| Summary: | 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. |
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