Vol. 2, No. 2, 2020
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Finite-dimensional reduction of a supercritical exponent equation

Mohamed Ben Ayed
Vol. 2 (2020), No. 2, 379–397
DOI: 10.2140/tunis.2020.2.379
Abstract

We present a finite-dimensional reduction for a supercritical exponent PDE. We reduce the existence of a solution of the problem

−Δu = K|u|4∕(n−2)+εu in Ω (with ε > 0),u = 0 on ∂Ω,

to finding a critical point of a function defined in some set V⊂ ℝN × ℝN × ΩN.

Keywords
critical points, PDE with supercritical exponent, finite-dimensional reduction
Mathematical Subject Classification 2010
Primary: 35J60, 35J65, 58E05
Milestones
Received: 16 October 2018
Revised: 21 February 2019
Accepted: 18 March 2019
Published: 2 August 2019
Authors
Mohamed Ben Ayed
Université de Sfax
Faculté des Sciences
Tunisia