Exactness Results for Generalized Ambrosetti-Brezis-Cerami Problem and Related One-dimensional Elliptic Equations
Date
2000-11-02
Authors
Addou, Idris
Benmezai, Abdelhamid
Bouguima, Sidi Mohammed
Mohammed, Derhab
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We consider the boundary problem
-(φp(u'))' = φα(u) + λφβ(u) in (0, 1)
u(0) = u(1) = 0
where φp(x) = |x|p-2 x, p, α, β > 1 and λ ∈ ℝ*. We give the exact number of solutions for all λ and most values of α, β, p > 1. In the particular case where 1 < β < p = 2 < α, we resolve completely a problem suggested by A. Ambrosetti, H. Brezis and G. Cerami and which was partially solved by S. Villegas.
Description
Keywords
Exactness, p-Laplacian, Concave-convex nonlinearities, Quadrature method
Citation
Addou, I., Benmezai, A., Bouguima, S. M., & Derhab, M. (2000). Exactness results for generalized Ambrosetti-Brezis-Cerami problem and related one-dimensional elliptic equations. <i>Electronic Journal of Differential Equations, 2000</i>(66), pp. 1-34.
Rights
Attribution 4.0 International