The Gelfand problem for the 1-homogeneous p-Laplacian
In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous p-Laplacian in a bounded domain ω ⊃ ℝ N , that is, we deal with (equation presented) in ω with u = 0 on δ ω. For this problem we show that, for p ϵ [2, ∞], there exists a positive critical value...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | JOUR |
| Materias: | |
| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_21919496_v8_n1_p545_Tapia |
| Aporte de: |
| Sumario: | In this paper, we study the existence of viscosity solutions to the Gelfand problem for the 1-homogeneous p-Laplacian in a bounded domain ω ⊃ ℝ N , that is, we deal with (equation presented) in ω with u = 0 on δ ω. For this problem we show that, for p ϵ [2, ∞], there exists a positive critical value λ ∗ = λ ∗ (ω, N, p) such that the following holds: • If λ λ ∗ , the problem admits a minimal positive solution wλ ∗ • If λ > λ ∗ , the problem admits no solution. Moreover, the branch of minimal solutions {wλ} is increasing with λ ∗ In addition, using degree theory, for fixed p we show that there exists an unbounded continuum of solutions that emanates from the trivial solution u = 0 with λ = 0, and for a small fixed λ we also obtain a continuum of solutions with p ϵ [2, ∞]. © 2019 Walter de Gruyter GmbH, Berlin/Boston 2019. |
|---|