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Multiple Solutions of Nonlinear Scalar Field Equations
Authors:
M
nica Clapp a;
Tobias Weth b
nica Clapp a;
Tobias Weth b
| Affiliations: | a Instituto de Matem ticas, Universidad Nacional Autnoma de M xico, Circuito Exterior, Ciudad Universitaria, Mxico, D.F., Mexico |
b Mathematisches Institut, Universit t Giessen, Giessen, Germany |
DOI:
10.1081/PDE-200037766
Publication Frequency:
12 issues per year
Published in:
Communications in Partial Differential Equations,
Volume
29,
Issue
9 &
10
January
2005
, pages 1533
- 1554
Communications in Partial Differential Equations,
Volume
29,
Issue
9 &
10
January
2005
, pages 1533
- 1554
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(English)
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Abstract
We establish existence of multiple solutions of the semilinear elliptic equation
 where N ≥ 3, 2 < p < 2N/(N - 2), and a(x) and q(x) tend to some positive limits a∞ and q∞ respectively as |x| → ∞. Assuming some weak one-sided asymptotic estimates for a(x) and q(x), we prove that (℘) has at least  pairs ±u of nontrivial weak solutions.
|
Keywords:
Nonlinear Schr dinger equations;
Lack of compactness;
Flow invariance;
Minimax methods
|
| Mathematics Subject Classification: 35J20; 35J60 |
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