Sign-changing solutions for a perturbed biharmonic equation with critical exponent

Rabeh Ghoudi () and Moufida Lahrach ()
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Rabeh Ghoudi: University of Gabes
Moufida Lahrach: University of Gabes

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-21

Abstract: Abstract This paper is concerned with the following nonlinear elliptic problem with critical exponent $$(P_\varepsilon )$$ ( P ε ) : $$\Delta ^{2} u= (1+\varepsilon K(x))|u|^{(8/(n-4))}u$$ Δ 2 u = ( 1 + ε K ( x ) ) | u | ( 8 / ( n - 4 ) ) u in $$ \Omega $$ Ω , $$\Delta u=u= 0$$ Δ u = u = 0 on $$\partial \Omega $$ ∂ Ω , where $$\Omega $$ Ω is a bounded smooth domain in $$\mathbb {R}^n$$ R n , $$n\ge 5$$ n ≥ 5 , $$\varepsilon $$ ε is a small positive parameter. We prove the existence of sign-changing solution in higher dimensions: to this aim we develop a general finite-dimensional reduction procedure for perturbed variational functionals.

Keywords: Biharmonic equation; Critical Sobolev exponent; Finite-dimensional reduction; Sign-changing solutions; 35J20; 35J60 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00355-w

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