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

Staněk, Svatoslav (1997)

Archivum Mathematicum

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.

On a differential-algebraic problem

Anita Dąbrowicz-Tlałka, Tadeusz Jankowski (2000)

Applications of Mathematics

The method of quasilinearization is a procedure for obtaining approximate solutions of differential equations. In this paper, this technique is applied to a differential-algebraic problem. Under some natural assumptions, monotone sequences converge quadratically to a unique solution of our problem.

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