Volume 2, Issue 6, December 2013, Page: 184-190
A Nonexistence of Solutions to a Supercritical Problem
Kamal Ould Bouh, Department of Mathematics, Taibah University, Almadinah Almunawwarah, KSA
Received: Dec. 4, 2013;       Published: Jan. 10, 2014
DOI: 10.11648/j.pamj.20130206.13      View  2668      Downloads  76
Abstract
In this paper, we study the nonlinear elliptic problem involving nearly critical exponent (P_ϵ ) ∶ -∆u=K u^(□((n+2)/(n-2))+ϵ) in Ω ; u >0 in Ω and u=0 on ∂ Ω where is a smooth bounded domain in 〖IR〗^n n≥3, K is a C^3positive function and ϵ is a small positive real parameter. We prove that, for small, (Pε) has no positive solutions which blow up at one critical point of the function K.
Keywords
Nonlinear Elliptic Equations, Critical Exponent, Variational Problem
To cite this article
Kamal Ould Bouh, A Nonexistence of Solutions to a Supercritical Problem, Pure and Applied Mathematics Journal. Vol. 2, No. 6, 2013, pp. 184-190. doi: 10.11648/j.pamj.20130206.13
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