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The Mountain Pass Theorem and Critical Points of Saddle Type

In: Methods in Nonlinear Integral Equations

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  • Radu Precup

    (Babeş-Bolyai University, Department of Applied Mathematics)

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)

Suggested Citation

  • Radu Precup, 2002. "The Mountain Pass Theorem and Critical Points of Saddle Type," Springer Books, in: Methods in Nonlinear Integral Equations, chapter 0, pages 111-127, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-9986-3_9
    DOI: 10.1007/978-94-015-9986-3_9
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