Higher-order Lidstone boundary value problems for elliptic partial differential equations

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 higherorder 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.  2005 Elsevier Inc. All rights reserved.Keywords: 2nth-order Lidstone boundary value problem; Existence and uniqueness; Method of upper and lower solutions; Monotone method ✩

On Coupled Systems of Lidstone-Type Boundary Value Problems

“…where m ≥ 1, λ > 0, and F is continuous at least in the interior of the domain of interest; in [11] the authors apply a different methodology to a similar Lidstone problem, analyzing the existence of solution via bifurcation techniques; in [3] it is studied the existence, multiplicity and nonexistence results for nontrivial solutions to a nonlinear discrete fourth-order Lidstone boundary value problem; in [6] Cid et al consider Lidstone boundary value problem, applying the monotone iterative technique with fixed point theorems of cone expansion or compression type; in [21] the authors deal with the existence and uniqueness of solution for a class of elliptic Lidstone boundary value problems; on [2,20], the authors study, respectively, Lidstone polynomials and boundary value problems and boundary layer phenomenon,...among others.…”