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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.


Documento: Artículo
Título:The Gelfand problem for the 1-homogeneous p-Laplacian
Autor:Tapia, J.C.; Salas, A.M.; Rossi, J.D.
Filiación:Departamento de Matemáticas, Universidad de Almería, Ctra. Sacramento s/n, La Cañada de San Urbano, Almería, 04120, Spain
Departamento de Análisis Matemático, Campus Fuentenueva S/N, Universidad de Granada, Granada, 18071, Spain
Departamento de Matemática, FCEyN, Universidad de Buenos Aires, Ciudad Universitaria, Pab 1 (1428), Buenos Aires, Argentina
Palabras clave:elliptic equations; Gelfand problem; viscosity solutions
Página de inicio:545
Página de fin:558
Título revista:Advances in Nonlinear Analysis
Título revista abreviado:Adv. Nonlinear Anal.


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---------- APA ----------
Tapia, J.C., Salas, A.M. & Rossi, J.D. (2019) . The Gelfand problem for the 1-homogeneous p-Laplacian. Advances in Nonlinear Analysis, 8(1), 545-558.
---------- CHICAGO ----------
Tapia, J.C., Salas, A.M., Rossi, J.D. "The Gelfand problem for the 1-homogeneous p-Laplacian" . Advances in Nonlinear Analysis 8, no. 1 (2019) : 545-558.
---------- MLA ----------
Tapia, J.C., Salas, A.M., Rossi, J.D. "The Gelfand problem for the 1-homogeneous p-Laplacian" . Advances in Nonlinear Analysis, vol. 8, no. 1, 2019, pp. 545-558.
---------- VANCOUVER ----------
Tapia, J.C., Salas, A.M., Rossi, J.D. The Gelfand problem for the 1-homogeneous p-Laplacian. Adv. Nonlinear Anal. 2019;8(1):545-558.