The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator
In this paper, we study the solution of nonlinear equation ΔkB(ΔB + m2)k u(x) = f(x,Δk-1B (ΔB + m2)ku(x)) where the operator ΔkB is the Bessel Laplace operator iterated k-times defined by ΔkB = (Bx1 + Bx2 + · · · + Bxn)k n is the dimension of the space R+n, x = (x1, x2,..., xn) E R+n, k is a positiv...
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th-cmuir.6653943832-509932018-09-04T04:49:32Z The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator S. Niyom A. Kananthai Mathematics In this paper, we study the solution of nonlinear equation ΔkB(ΔB + m2)k u(x) = f(x,Δk-1B (ΔB + m2)ku(x)) where the operator ΔkB is the Bessel Laplace operator iterated k-times defined by ΔkB = (Bx1 + Bx2 + · · · + Bxn)k n is the dimension of the space R+n, x = (x1, x2,..., xn) 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 Δk-1B (ΔB+m2)ku(x). Moreover such solution u(x) related to the nonhomogeneous Bessel biharmonic equation depend on the conditions of k. 2018-09-04T04:49:32Z 2018-09-04T04:49:32Z 2010-06-29 Journal 1312885X 2-s2.0-77953900558 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77953900558&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50993 |
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Mathematics |
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Mathematics S. Niyom A. Kananthai The nonlinear product of the Bessel Laplace operator and the Bessel Helmholtz operator |
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In this paper, we study the solution of nonlinear equation ΔkB(ΔB + m2)k u(x) = f(x,Δk-1B (ΔB + m2)ku(x)) where the operator ΔkB is the Bessel Laplace operator iterated k-times defined by ΔkB = (Bx1 + Bx2 + · · · + Bxn)k n is the dimension of the space R+n, x = (x1, x2,..., xn) 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 Δk-1B (ΔB+m2)ku(x). Moreover such solution u(x) related to the nonhomogeneous Bessel biharmonic equation depend on the conditions of k. |
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Journal |
| author |
S. Niyom A. Kananthai |
| author_facet |
S. Niyom A. Kananthai |
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S. Niyom |
| 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 |
2018 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=77953900558&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/50993 |
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