Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4643390 | Journal of Computational and Applied Mathematics | 2006 | 12 Pages |
Abstract
We consider the differential equation ℓ(u)=F(u)ℓ(u)=F(u), where ℓℓ is a formally self-adjoint second-order differential expression and F is nonlinear, with nonlinear boundary conditions. Under appropriate assumptions on ℓ,Fℓ,F and the boundary conditions, existence of solutions is established using the method of lower and upper solutions. A generalized quasilinearization method is then developed for this problem and we obtain two monotonic sequences of approximate solutions converging quadratically to a solution of the equation.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Mohamed El-Gebeily, Donal O’Regan,