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 | References | Similar Articles | Additional Information

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