Displaying similar documents to “The generalized boundary value problem is a Fredholm mapping of index zero”

On the generalized boundary value problem

Boris Rudolf (2000)

Archivum Mathematicum

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In the paper it is proved that the generalized linear boundary value problem generates a Fredholm operator. Its index depends on the number of boundary conditions. The existence results of Landesman-Lazer type are given as an application to nonlinear problems by using dual generalized boundary value problems.

Fixed points and solutions of boundary value problems at resonance

Alaa Almansour, Paul Eloe (2015)

Annales Polonici Mathematici

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We consider a simple boundary value problem at resonance for an ordinary differential equation. We employ a shift argument and construct a regular fixed point operator. In contrast to current applications of coincidence degree, standard fixed point theorems are applied to give sufficient conditions for the existence of solutions. We provide three applications of fixed point theory. They are delicate and an application of the contraction mapping principle is notably missing. We give a...