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

Authors
  • Staněk, Svatoslav
Publication Date
Jan 01, 1997
Source
Czech Digital Mathematics Library
Keywords
Language
English
License
Unknown
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Abstract

summary:A class of functional boundary conditions for the second order functional differential equation $x''(t)=(Fx)(t)$ is introduced. Here $F:C^1(J) \rightarrow L_1(J)$ 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.

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