Affiliation:
1. School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, P.R. China
2. College of Mathematics, Changchun Normal University, Changchun, 130032, P.R. China
Abstract
In this paper, a class of ( p , q )-Laplacian equations with critical growth is taken into consideration: − Δ p u − Δ q u + ( | u | p − 2 + | u | q − 2 ) u + λ ϕ | u | q − 2 u = μ g ( u ) + | u | q ∗ − 2 u , x ∈ R 3 , − Δ ϕ = | u | q , x ∈ R 3 , where Δ ξ u = div ( | ∇ u | ξ − 2 ∇ u ) is the ξ-Laplacian operator ( ξ = p , q ), 3 2 < p < q < 3, λ and μ are positive parameters, q ∗ = 3 q / ( 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.
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