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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Multiple Solutions for a Class
of Semilinear Elliptic Equations


Author: Zhiren Jin
Journal: Proc. Amer. Math. Soc. 125 (1997), 3659-3667
MSC (1991): Primary 35J65, 35J25
MathSciNet review: 1443158
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Abstract: We show that for a class of semilinear elliptic equations there are at least three nontrivial solutions. Existence of infinitely many solutions is also shown when the nonlinear term is odd. In our results, the nonlinear term can grow super-critically at infinity.


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Additional Information

Zhiren Jin
Email: zhiren@cs.twsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-97-04199-3
PII: S 0002-9939(97)04199-3
Keywords: Multiple solutions, semilinear elliptic equations, sub- super-solutions, variational method, pseudo-gradient flow, local minimum of a functional
Received by editor(s): July 16, 1996
Communicated by: Jeffrey B. Rauch
Article copyright: © Copyright 1997 American Mathematical Society