Positive solutions of the p-Laplace Emden-Fowler equation in hollow thin symmetric domains

Title:

Positive solutions of the p-Laplace Emden-Fowler equation in hollow thin symmetric domains

Creator:

Kajikiya, Ryuji

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c28371f8-2fae-4a6d-b40b-6d171a488405
uuid:c28371f8-2fae-4a6d-b40b-6d171a488405
doi:10.21136/MB.2014.143845

Subject:

Emden-Fowler equation, group invariant solution, least energy solution, positive solution, and variational method

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study the existence of positive solutions for the p-Laplace Emden-Fowler equation. Let H and G be closed subgroups of the orthogonal group O(N) such that H G ⊂ O(N). We denote the orbit of G through x ∈ R N by G(x), i.e., G(x) := {gx: g ∈ G}. We prove that if H(x) G(x) for all x ∈ Ω and the first eigenvalue of the p-Laplacian is large enough, then no H invariant least energy solution is G invariant. Here an H invariant least energy solution means a solution which achieves the minimum of the Rayleigh quotient among all H invariant functions. Therefore there exists an H invariant G non-invariant positive solution.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

145-154

Source:

Mathematica bohemica | 2014 Volume:139 | Number:2

Harvested from:

CDK

Metadata only:

false