This article is concerned with the following nonlinear supercritical elliptic problem:− M (‖∇
u‖ 2 2) Δ u= f (x, u), in B 1 (0), u= 0, on∂ B 1 (0), where B 1 (0) is the unit ball in R 2, M …

In this paper, we first deduce the following Sobolev inequality with logarithmic term:(0.1)
sup⁡{∫ B| u| 2⁎| ln⁡(τ+| u|)|| x| β dx: u∈ H 0, rad 1 (B),‖∇ u‖ L 2 (B)= 1}<∞, where β> 0 …

In this paper, we obtain several Adams-type inequalities with logarithmic weights on the unit
ball B in R n, where n≥ 3. Firstly, we show that for any β∈ 0, 1, the following critical Adams' …

A Sobolev type embedding for radially symmetric functions on the unit ball B in R n, n≥ 3,
into the variable exponent Lebesgue space L 2⋆+| x| α (B), 2⋆= 2 n/(n− 2), α> 0, is known …

This paper studies the existence of nontrivial solutions to the following class of Schrödinger
equations:{− div (w (x)∇ u)= f (x, u), x∈ B 1 (0), u= 0, x∈∂ B 1 (0), where w (x)=(ln (1/| x|)) β …

In this paper, we consider a class of Schrödinger-Poisson systems on bounded domains that
depend on a parameter η. These systems have variable supercritical exponents and a …

Supercritical Trudinger-Moser inequalities with logarithmic weights in dimension two Page 1
http://www.aimspress.com/journal/Math AIMS Mathematics, 8(8): 18354–18372. DOI:10.3934/math.2023933 …

We obtain some sharp weighted version of Adams' inequality on second order Sobolev
spaces with Navier boundary conditions. The weights that we consider determine a …

In this paper, we study the existence of extremals for the following singular critical Trudinger–
Moser inequality with logarithmic weights: sup u∈ W 0, r 1, n (B, ω β), u ω β≤ 1∫ B exp (α …

Our main goal is to investigate supercritical Hardy-Sobolev type inequalities with a
logarithmic term and their corresponding variational problem. We prove the existence of …