Cotsiolis, AthanaseLabropoulos, Nikos2021-08-182021-08-182007-11-30Cotsiolis, 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. 1-18.1072-6691https://hdl.handle.net/10877/14378Following 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).Text18 pages1 file (.pdf)enAttribution 4.0 InternationalNeumann problemq-LaplacianSolid torusNo radial symmetryCritical of supercritical exponentArticle