Weak linking theorems and Schrödinger equations with critical Sobolev exponent

Schechter, Martin; Zou, Wenming

doi:10.1051/cocv:2003029

Schechter, Martin ; Zou, Wenming

ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 601-619

Voir la notice de l'article provenant de la source Numdam

Résumé

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 $- Δ u + V (x) u = {K (x) | u |}^{2^{*} - 2} u + g (x, u), u \in W^{1, 2} (𝐑^{N})$ , where $N \geq 4; V, K, g$ are periodic in $x_{j}$ for $1 \leq j \leq N$ and 0 is in a gap of the spectrum of $- Δ + V$ ; $K > 0$ . If $0 < g (x, u) u \leq {c | u |}^{2^{*}}$ for an appropriate constant $c$ , we show that this equation has a nontrivial solution.

MR

DOI : 10.1051/cocv:2003029

Classification : 35B33, 35J65, 35Q55
Keywords: linking, Schrödinger equations, critical Sobolev exponent

@article{COCV_2003__9__601_0,
     author = {Schechter, Martin and Zou, Wenming},
     title = {Weak linking theorems and {Schr\"odinger} equations with critical {Sobolev} exponent},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {601--619},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2003},
     doi = {10.1051/cocv:2003029},
     mrnumber = {1998717},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003029/}
}

TY  - JOUR
AU  - Schechter, Martin
AU  - Zou, Wenming
TI  - Weak linking theorems and Schrödinger equations with critical Sobolev exponent
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2003
SP  - 601
EP  - 619
VL  - 9
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003029/
DO  - 10.1051/cocv:2003029
LA  - en
ID  - COCV_2003__9__601_0
ER  -

%0 Journal Article
%A Schechter, Martin
%A Zou, Wenming
%T Weak linking theorems and Schrödinger equations with critical Sobolev exponent
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2003
%P 601-619
%V 9
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2003029/
%R 10.1051/cocv:2003029
%G en
%F COCV_2003__9__601_0

Schechter, Martin; Zou, Wenming. Weak linking theorems and Schrödinger equations with critical Sobolev exponent. ESAIM: Control, Optimisation and Calculus of Variations, Tome 9 (2003), pp. 601-619. doi: 10.1051/cocv:2003029

Cité par Sources :

Parcourir par

Geodesic

Parcourir par