International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2005 / Article

Open Access

Volume 2005 |Article ID 561415 | https://doi.org/10.1155/IJMMS.2005.3405

M. Hesaaraki, B. Raessi, "Existence of solutions for a family of polyharmonic and biharmonic equations", International Journal of Mathematics and Mathematical Sciences, vol. 2005, Article ID 561415, 13 pages, 2005. https://doi.org/10.1155/IJMMS.2005.3405

Existence of solutions for a family of polyharmonic and biharmonic equations

Received17 Apr 2005
Revised28 Sep 2005

Abstract

We consider a family of polyharmonic problems of the form (Δ)mu=g(x,u) in Ω, Dαu=0 on Ω, where Ωn is a bounded domain, g(x,)L(Ω), and |α|<m. By using the fibering method, we obtain some results about the existence of solution and its multiplicity under certain assumptions on g. We also consider a family of biharmonic problems of the form Δ2u+(Δϕ+|ϕ|2)Δu+2ϕΔu=g(x,u), where ϕC2(Ω¯), and Ω, g, and the boundary condition are the same as above. For this problem, we prove the existence and multiplicity of solutions too.

Copyright © 2005 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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