Tunisian Journal of Mathematics

Finite-dimensional reduction of a supercritical exponent equation

Mohamed Ben Ayed

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

Δ u = K | u | 4 ( n 2 ) + ε u  in  Ω  (with  ε > 0 ) , u = 0  on  Ω ,

to finding a critical point of a function defined in some set VN×N×ΩN.

Article information

Tunisian J. Math., Volume 2, Number 2 (2020), 379-397.

Received: 16 October 2018
Revised: 21 February 2019
Accepted: 18 March 2019
First available in Project Euclid: 13 August 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 35J60: Nonlinear elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations 58E05: Abstract critical point theory (Morse theory, Ljusternik-Schnirelman (Lyusternik-Shnirel m an) theory, etc.)

critical points PDE with supercritical exponent finite-dimensional reduction


Ben Ayed, Mohamed. Finite-dimensional reduction of a supercritical exponent equation. Tunisian J. Math. 2 (2020), no. 2, 379--397. doi:10.2140/tunis.2020.2.379. https://projecteuclid.org/euclid.tunis/1565661722

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