## Abstract For the __n__th order nonlinear differential equation, __y__^(__n__)^ = __f__(__x__, __y__, __y__′, …, __y__^(__n__−1)^), we consider uniqueness implies existence results for solutions satisfying certain (__k__ + __j__)‐point boundary conditions, 1 ⩽ __j__ ⩽ __n__ − 1, and 1 ⩽ __k__ ⩽ _
Existence implies uniqueness for a class of singular anisotropic elliptic boundary value problems
✍ Scribed by Florica Şt. Cîrstea; Vicenţiu D. Radulescu
- Publisher
- John Wiley and Sons
- Year
- 2001
- Tongue
- English
- Weight
- 89 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.241
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✦ Synopsis
Abstract
We consider a singular anisotropic quasilinear problem with Dirichlet boundary condition and we establish two sufficient conditions for the uniqueness of the solution, provided such a solution exists. The proofs use elementary tools and they are based on a general comparison lemma combined with the generalized mean value theorem. Copyright © 2001 John Wiley & Sons, Ltd.
📜 SIMILAR VOLUMES
Strong solvability in the Sobolev space W 2 p is proved for the oblique derivative problem almost everywhere in ∂u/∂ + σ x u = ϕ x in the trace sense on ∂ in the case when the vector field x has a contact of infinite order with ∂ at the points of some non-empty subset E ⊂ ∂ .