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From Convexity to Nonconvexity pp 333–344Cite as

Mountain Pass Theorems, Deformation Theorems, and Palais-Smale Conditions

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Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 55))

Abstract

Let E be a Banach space, X ⊂ E be an open subset, f ∈ C 1 (X, R) be a functional and

$$\begin{array}{*{20}{c}} {K = \left\{ {x \in X:f'\left( x \right) = 0} \right\},} \\ {{K_c} = \left\{ {x \in X:f\left( x \right) = c,f'\left( x \right) = 0} \right\}} \end{array}$$

are the sets of critical points of f.

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Authors and Affiliations

  1. Centre of Applied Mathematics and Informatics, University of Rousse, Rousse, 7017, Bulgaria

    Stepan A. Tersian

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  1. Stepan A. Tersian
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Editor information

Editors and Affiliations

  1. University of Delaware, USA

    R. P. Gilbert

  2. University of Florida, USA

    P. M. Pardalos

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© 2001 Kluwer Academic Publishers

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Tersian, S.A. (2001). Mountain Pass Theorems, Deformation Theorems, and Palais-Smale Conditions. In: Gilbert, R.P., Panagiotopoulos, P.D., Pardalos, P.M. (eds) From Convexity to Nonconvexity. Nonconvex Optimization and Its Applications, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0287-2_24

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  • DOI: https://doi.org/10.1007/978-1-4613-0287-2_24

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7979-9

  • Online ISBN: 978-1-4613-0287-2

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