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Multiple Solutions for a Class of Semilinear Elliptic Equations
Author(s):
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.
References:
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- 2.
- Ambrosetti, A., Brezis, H. & Cerami, G., Combined effects of concave and convex nonlinearities in some elliptic problems, J. Funct. Anal. 122 (1994), 519-543. MR 95g:35059
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- Ambrosetti, A. & Rabinowitz, P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal. 14 (1973), 349-381. MR 51:6412
- 4.
- Brezis, H. & Nirenberg, L.,
 versus  local minimizers, C.R. Acad. Sci. Paris 317 (1993), 465-472. MR 94g:49044 - 5.
- Ghoussoub, N. & Preiss, D., A general mountain pass principle for locating and classifying critical points, Ann. Inst. H. Poincaré Anal. Non Linéaire 6 (1989), 321-330. MR 91a:58043
- 6.
- Gilbarg, D. & Trüdinger, N.S., Elliptic partial differential equations of second order, second edition, Springer-verlag (1983). MR 86c:35035
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Additional Information:
Zhiren
Jin
Affiliation:
Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260
Email:
zhiren@cs.twsu.edu
DOI:
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
Copyright of article:
Copyright
1997,
American Mathematical Society
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