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Multiple nontrivial solutions of resonant and nonresonant asymptotically linear problems


Author: Shair Ahmad
Journal: Proc. Amer. Math. Soc. 96 (1986), 405-409
MSC: Primary 35J65; Secondary 35B32
DOI: https://doi.org/10.1090/S0002-9939-1986-0822429-2
MathSciNet review: 822429
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Abstract: We give simple conditions under which a second order semilinear elliptic boundary value problem with the zero solution has at least two nonzero solutions. Our conditions involve the change in the spectrum of the linearization of the problem going from zero to infinity.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1986-0822429-2
Keywords: Critical point of mountain-pass type, Leray-Schauder degree, eigenvalues, nondegenerate critical point, Landesman-Lazer condition
Article copyright: © Copyright 1986 American Mathematical Society

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