Proceedings of the American Mathematical Society · 1985 · 10 citations · 2 references
Natural SciencesMathematicsApplied MechanicsDifferential EquationsFluid DynamicsBoundary ConditionsBoundary-value ProblemsExistence TheoryInitial Value ProblemsPartial Differential EquationsVariational FormulationDirichlet ConditionsDirichlet ProblemsElliptic Boundary-value ProblemsLeast Action PrincipleMultipoint Boundary Value ProblemsNonlinear Boundary-value ProblemsParabolic Boundary-value ProblemsTwo-point Boundary Value Problems
The dual least action principle is used to prove a necessary and sufficient condition for the solvability of a Dirichlet problem of the form u" + u + f(x, u) = 0, u(0) = u(tr) = 0 when/(.x,) is nondecreasing and /("/(v, v) dv satisfies a suitable growth condition.
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