A Neumann problem with the q-Laplacian on a solid torus in the critical of supercritical case
Date
2007-11-30
Authors
Cotsiolis, Athanase
Labropoulos, Nikos
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University-San Marcos, Department of Mathematics
Abstract
Following the work of Ding [21] we study the existence of a non-trivial positive solution to the nonlinear Neumann problem
Δqu + α(x)uq-1 = λƒ(x)up-1, u > 0 on T,
∇u|q-2 ∂u/∂v + b(x)uq-1 = λg(x)up̃-1 on ∂T,
p = 2q/2-q > 6, p̃ = q/2-q > 4, 3/2 < q < 2,
on a solid torus of ℝ3. When data are invariant under the group G = O(2) x I ⊂ O(3), we find solutions that exhibit no radial symmetries. First we find the best constants in the Sobolev inequalities for the supercritical case (the critical of supercritical).
Description
Keywords
Neumann problem, q-Laplacian, Solid torus, No radial symmetry, Critical of supercritical exponent
Citation
Cotsiolis, A., & Labropoulos, N. (2007). A Neumann problem with the q-Laplacian on a solid torus in the critical of supercritical case. <i>Electronic Journal of Differential Equations, 2007</i>(164), pp. 1-18.
Rights
Attribution 4.0 International