Transactions of the American Mathematical Society · 1950 · 35 citations · 4 references
Natural SciencesMathematicsDifferential EquationsFunctional AssessmentFunctional RestorationExistence TheoremsExistence TheoryIntegral EquationsPartial Differential EquationsSystems Of Differential EquationsBranch PointsElliptic Partial Differential EquationsLocal Existence TheoryMultiplicity Theory
local solutions of an abstract functional equation was defined and studied. The theory developed was used to obtain existence theorems for integral equations and elliptic differential equations. The purpose of this paper is to extend the multiplicity theory and apply the new results to obtain more existence theorems for integral and differential equations. We study the equation in a Banach space X,
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