Abstract
The aim of this paper is to show the existence and uniqueness of a solution for a class of 2nth-order elliptic Lidstone boundary value problems where the nonlinear functions depend on the higher-order derivatives. Sufficient conditions are given for the existence and uniqueness of a solution. It is also shown that there exist two sequences which converge monotonically from above and below, respectively, to the unique solution. The approach to the problem is by the method of upper and lower solutions together with monotone iterative technique for nonquasimonotone functions. All the results are directly applicable to 2nth-order two-point Lidstone boundary value problems.
| Original language | English |
|---|---|
| Pages (from-to) | 314-333 |
| Number of pages | 20 |
| Journal | Journal of Mathematical Analysis and Applications |
| Volume | 308 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Aug 2005 |
Keywords
- 2nth-order Lidstone boundary value problem
- Existence and uniqueness
- Method of upper and lower solutions
- Monotone method