Upper and Lower Solution Methods for Fully Nonlinear Boundary Value Problems

By Jeffrey Ehme, Paul W. Eloe, J. Henderson. 2002

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Fourth-order problems with nonlinear boundary conditions (2005, methodology): “In [7] because of the dependence on odd derivatives, the authors employ the Kamke existence of solutions of initial value problems theorem [12].”
Positive fixed points and fourth‐order equations (2009, methodology): “2): lower and upper solutions [5, 9, 10, 19], monotone iterative technique [2, 11, 13], Krasnoselskii fixed point theorem [6], fixed point index [3, 16, 18, 24], Leray–Schauder degree [12, 14], variational methods [8, 21] and bifurcation theory [17, 20].”
Unbounded upper and lower solutions method for Sturm–Liouville boundary value problem on infinite intervals (2009, unknown): “It is well know that the upper and lower solution method is a powerful tool to prove the existence of solutions to a differential equation subject to certain boundary value problem, see [2–6,10–12] and the reference therein.”