The Mountain Pass Theorem and Critical Points of Saddle Type

Radu Precup
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Radu Precup: Babeş-Bolyai University, Department of Applied Mathematics

Chapter Chapter 8 in Methods in Nonlinear Integral Equations, 2002, pp 111-127 from Springer

Abstract: Abstract In Chapter 9 we shall continue the investigation of the L p solutions of the Hammerstein integral equations under the assumption that f (x, 0) = 0, that is, the null function is a solution. We are now interested in non-null solutions. The technique we use is based on the so called mountain pass theorem of Ambrosetti-Rabinowitz [3]. By this method one can establish the existence of a critical point u of the functional E which in general is not an extremum point of E, and has the property that in any neighborhood of u there are points v and w with E (v)

Keywords: Banach Space; Convergent Subsequence; Critical Point Theory; Mountain Pass Theorem; Saddle Type (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1007/978-94-015-9986-3_9

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