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- W4381378082 abstract "Abstract We will consider the following problem: -Δu + u = f(u), x ∈ Ω, u > 0, x ∈ Ω, ∂u/∂ν = 0, x ∈ ∂Ω, where Ω is a bounded annulus in ℝ^N (N ≥ 3), and the function f has either exponential growth given by the Trudinger-Moser inequality f(u) = u(e^{u^2}-1), or it is of the power form f(u) = u|u|^{p-2}, where p is supercritical. It is known that this problem always has a positive radial solution. Our main goal in this paper is to prove the existence of a positive non-radial solution for the case f(u) = u(e^{u^2}-1), and to establish the multiplicity of non-radial positive solutions for the case f(u) = u|u|^{p-2} when the annulus is thin. We shall first state our results for a general annulus when the right hand side of equation is of the form a(x) f(u) where the function a(x) belongs to a class of sufficiently smooth non-negative functions which enjoys certainsymmetry and monotonicity properties. This class includes the case where the function a is radial." @default.
- W4381378082 created "2023-06-21" @default.
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- W4381378082 date "2023-06-20" @default.
- W4381378082 modified "2023-09-23" @default.
- W4381378082 title "A Neumann problem with supercritical and exponential growth in dimension N ≥ 3" @default.
- W4381378082 doi "https://doi.org/10.21203/rs.3.rs-3069438/v1" @default.
- W4381378082 hasPublicationYear "2023" @default.
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