We investigate the existence and concentration of normalized solutions for a p-Laplacian problem with logarithmic nonlinearity of type {−εpΔpu+V(x)|u|p−2u=λ|u|p−2u+|u|p−2ulog|u|pinRN,∫RN|u|pdx=apεN, where a,ε>0, λ∈R is known as the Lagrange multiplier, Δp⋅=div(|∇⋅|p−2∇⋅) denotes the usual p-Laplacian operator with 2≤p
Shen, L., Squassina, M., Existence and concentration of normalized solutions for p-Laplacian equations with logarithmic nonlinearity, <<JOURNAL OF DIFFERENTIAL EQUATIONS>>, 2025; 421 (N/A): 1-49. [doi:10.1016/j.jde.2024.11.049] [https://hdl.handle.net/10807/311879]
Existence and concentration of normalized solutions for p-Laplacian equations with logarithmic nonlinearity
Squassina, Marco
2025
Abstract
We investigate the existence and concentration of normalized solutions for a p-Laplacian problem with logarithmic nonlinearity of type {−εpΔpu+V(x)|u|p−2u=λ|u|p−2u+|u|p−2ulog|u|pinRN,∫RN|u|pdx=apεN, where a,ε>0, λ∈R is known as the Lagrange multiplier, Δp⋅=div(|∇⋅|p−2∇⋅) denotes the usual p-Laplacian operator with 2≤p
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