A global implicit function theorem and its applications to functional equations

Dariusz Idczak

doi:10.3934/dcdsb.2014.19.2549

Article Contents

2014, Volume 19, Issue 8: 2549-2556. Doi: 10.3934/dcdsb.2014.19.2549

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A global implicit function theorem and its applications to functional equations

Dariusz Idczak^1,

1.
Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz

Received: September 30, 2013

Revised: February 28, 2014

Published: September 2014

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Abstract

The main result of the paper is a global implicit function theorem. In the proof of this theorem, we use a variational approach and apply Mountain Pass Theorem. An assumption guarantying existence of an implicit function on the whole space is a Palais-Smale condition. Some applications to differential and integro-differential equations are given.

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Mathematics Subject Classification: Primary: 26B10, 47J07.

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References

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