| Issue |
ESAIM: COCV
Volume 9, February 2003
|
|
|---|---|---|
| Page(s) | 601 - 619 | |
| DOI | https://doi.org/10.1051/cocv:2003029 | |
| Published online | 15 September 2003 | |
Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent
1
Department of Mathematics, University of California,
Irvine, CA 92697-3875, USA; mschecht@math.uci.edu.
2
Department of Mathematical Sciences, Tsinghua University,
Beijing 100084, China; wzou@math.tsinghua.edu.cn.
Received:
28
October
2002
In this paper we establish a variant
and generalized weak linking
theorem, which contains more delicate result and insures the existence of
bounded
Palais–Smale sequences of a strongly indefinite functional.
The abstract result will be used to study the
semilinear Schrödinger equation 
, where N ≥ 4; V,K,g are periodic
in xj for 1 ≤ j ≤ N and 0 is in a gap of the spectrum
of -Δ + V; K>0. If 
for an
appropriate constant c, we show that this equation has a
nontrivial solution.
Mathematics Subject Classification: 35B33 / 35J65 / 35Q55
Key words: Linking / Schrödinger equations / critical Sobolev exponent.
© EDP Sciences, SMAI, 2003
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