MATHEMATICA BOHEMICA, Vol. 139, No. 4, pp. 699-711, 2014

Two notions which affected nonlinear analysis (Bernard Bolzano lecture)

Pavel Drábek

Pavel Drábek, Department of Mathematics and New Technologies for the Information Society (NTIS), University of West Bohemia, Univerzitní 22, 306 14 Plzeň, Czech Republic, e-mail:

Abstract: General mathematical theories usually originate from the investigation of particular problems and notions which could not be handled by available tools and methods. The Fučík spectrum and the $p$-Laplacian are typical examples in the field of nonlinear analysis. The systematic study of these notions during the last four decades led to several interesting and surprising results and revealed deep relationship between the linear and the nonlinear structures. This paper does not provide a complete survey. We focus on some pioneering works and present some contributions of the author. From this point of view the list of references is by no means exhaustive.

Keywords: Fučík spectrum; $p$-Laplacian

Classification (MSC 2010): 35J92, 34B15, 34B99, 35P30

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