1. Positive solutions of the p-Laplace Emden-Fowler equation in hollow thin symmetric domains
- Creator:
- Kajikiya, Ryuji
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Emden-Fowler equation, group invariant solution, least energy solution, positive solution, and variational method
- Language:
- English
- 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.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public