ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXVI, 1 (2007)
p. 85 - 98
The p-Laplacian - Mascot of Nonlinear Analysis
P. Drabek
Abstract.
In this paper we give survey of the results concerning the solvability of certain quasilinear
boundary value problems which contain the p-Laplacian as a main part. Special attention is paid
to the resonance problems which lead naturally to the study of spectral properties of nonlinear
operators. Besides statements of principal results in the historical context we also mention some
open problems which seem to be a great challenge for nonlinear analysts.
Keywords.
The p-Laplacian, nonlinear spectral analysis, nonlinear Fredholm alternative,
bifurcation from infinity.
AMS Subject classification. Primary: 35R35, 49M15, 49N50.
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Acta Mathematica Universitatis Comenianae
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