Abstract
Existence theory is developed for the equation l (u) = F(u), where l is a formally self-adjoint singular second-order differential expression and F is nonlinear. The problem is treated in a Hilbert space and we do not require the operators induced by l to have completely continuous resolvents. Nonlinear boundary conditions are allowed. Also, F is assumed to be weakly continuous and monotone at one point. Boundary behavior of functions associated with the domains of definitions of the operators associated with l in the singular case is investigated. A special class of self-adjoint operators associated with E is obtained. (c) 2006 Elsevier Inc. All rights reserved.
| Original language | English (Ireland) |
|---|---|
| Pages (from-to) | 140-156 |
| Number of pages | 17 |
| Journal | Journal Of Mathematical Analysis And Applications |
| Volume | 334 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1 Oct 2007 |
Keywords
- Galerkin method
- Monotone operators
- Nonlinear boundary conditions
- Nonlinear singular differential equations
Authors (Note for portal: view the doc link for the full list of authors)
- Authors
- El-Gebeily, M,O'Regan, D
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