Displaying similar documents to “Multiple solutions to a boundary value problem for an n-th order nonlinear difference equation.”

On a criterion for the existence of at least four solutions of functional boundary value problems

Staněk, Svatoslav (1997)

Archivum Mathematicum

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A class of functional boundary conditions for the second order functional differential equation x ' ' ( t ) = ( F x ) ( t ) is introduced. Here F : C 1 ( J ) L 1 ( J ) is a nonlinear continuous unbounded operator. Sufficient conditions for the existence of at least four solutions are given. The proofs are based on the Bihari lemma, the topological method of homotopy, the Leray-Schauder degree and the Borsuk theorem.