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Multiple solutions for the $ p$-Laplacian under global nonresonance


Authors: Manuel A. del Pino and Raúl F. Manásevich
Journal: Proc. Amer. Math. Soc. 112 (1991), 131-138
MSC: Primary 34B15
DOI: https://doi.org/10.1090/S0002-9939-1991-1045589-1
MathSciNet review: 1045589
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Abstract: Via the study of a simple Dirichlet boundary value problem associated with the one-dimensional $ p$-Laplacian, $ p > 1$, we show that in globally nonresonant problems for this differential operator the number of solutions may be arbitrarily large when $ p \in (1,\infty )\backslash \{ 2\} $. From this point of view $ p = 2$ turns out to be a very special case.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1991-1045589-1
Keywords: Nonresonance, multiple solutions
Article copyright: © Copyright 1991 American Mathematical Society

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