Nodal solutions to (p,q)-Laplacian equations with critical growth

Article type: Research Article

Authors: Pu, Hongling^a | Liang, Sihua^b | Ji, Shuguan^{a; *}

Affiliations: [a] School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, P.R. China | [b] College of Mathematics, Changchun Normal University, Changchun, 130032, P.R. China

Correspondence: [*] Corresponding author. E-mail: jishuguan@hotmail.com.

Abstract: In this paper, a class of (p,q)-Laplacian equations with critical growth is taken into consideration: −Δpu−Δqu+(|u|p−2+|u|q−2)u+λϕ|u|q−2u=μg(u)+|u|q∗−2u,x∈R3,−Δϕ=|u|q,x∈R3, where Δξu=div(|∇u|ξ−2∇u) is the ξ-Laplacian operator (ξ=p,q), 32<p<q<3, λ and μ are positive parameters, q∗=3q/(3−q) is the Sobolev critical exponent. We use a primary technique of constrained minimization to determine the existence, energy estimate and convergence property of nodal (that is, sign-changing) solutions under appropriate conditions on g, and thus generalize the existing results.

Keywords: (p, q)-Laplacian operator, Poisson equation, Critical growth, Variational methods, Nodal solutions

DOI: 10.3233/ASY-231871

Journal: Asymptotic Analysis, vol. 136, no. 2, pp. 133-156, 2024