Abstract
In this work, we study a class of Euler functionals defined in Banach spaces, associated with quasilinear elliptic problems involving p-Laplace operator (p > 2). First we obtain perturbation results in the spirit of the remarkable paper by Marino and Prodi (Boll. U.M.I. (4) 11(Suppl. fasc. 3): 1–32, 1975), using the new definition of nondegeneracy given in (Ann. Inst. H. Poincaré: Analyse Non Linéaire. 2:271–292, 2003). We also extend Morse index estimates for minimax critical points, introduced by Lazer and Solimini (Nonlinear Anal. T.M.A. 12:761–775, 1988) in the Hilbert case, to our Banach setting.
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Mathematics Subject Classification (1991) 58E05, 35B20, 35J60, 35J70
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Cingolani, S., Vannella, G. Marino—Prodi perturbation type results and Morse indices of minimax critical points for a class of functionals in Banach spaces. Annali di Matematica 186, 155–183 (2007). https://doi.org/10.1007/s10231-005-0176-2
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DOI: https://doi.org/10.1007/s10231-005-0176-2