Proceedings of the American Mathematical Society · 1999 · 63 citations · 20 references
Natural SciencesMathematicsComputational Fluid DynamicsDifferential EquationsFinite Element MethodsBoundary ConditionsBoundary-value ProblemsExistence TheoryInitial Value ProblemsPartial Differential EquationsElliptic Boundary-value ProblemsElliptic Partial Differential EquationsNonlinear Boundary-value ProblemsTwo-point Boundary Value ProblemsTwo-point Boundary-value FormulationUniqueness In Nonlinear Differential EquationsUniqueness Of Solutions
This paper is concerned with the existence and uniqueness of a solution for a class of fourth-order elliptic boundary value problems. The existence of a solution is proven by the method of upper and lower solutions without any monotone nondecreasing or nonincreasing property of the nonlinear function. Sufficient conditions for the uniqueness of a solution and some techniques for the construction of upper and lower solutions are given. All the existence and uniqueness results are directly applicable to fourth-order two-point boundary value problems.
20