# Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 9, page 601-619
- ISSN: 1292-8119

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topSchechter, Martin, and Zou, Wenming. "Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 601-619. <http://eudml.org/doc/90713>.

@article{Schechter2010,

abstract = {
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 $-\Delta
u+V(x)u=K(x)|u|^\{2^\ast-2\}u+g(x, u),
u\in W^\{1,2\}(\{\bf R\}^N)$, 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 $0<g(x, u)u\leq c|u|^\{2^\ast\}$ for an
appropriate constant c, we show that this equation has a
nontrivial solution.
},

author = {Schechter, Martin, Zou, Wenming},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Linking; Schrödinger equations; critical Sobolev exponent.; linking; critical Sobolev exponent},

language = {eng},

month = {3},

pages = {601-619},

publisher = {EDP Sciences},

title = {Weak Linking Theorems and Schrödinger Equations with Critical Sobolev Exponent},

url = {http://eudml.org/doc/90713},

volume = {9},

year = {2010},

}

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

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 601

EP - 619

AB -
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 $-\Delta
u+V(x)u=K(x)|u|^{2^\ast-2}u+g(x, u),
u\in W^{1,2}({\bf R}^N)$, 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 $0<g(x, u)u\leq c|u|^{2^\ast}$ for an
appropriate constant c, we show that this equation has a
nontrivial solution.

LA - eng

KW - Linking; Schrödinger equations; critical Sobolev exponent.; linking; critical Sobolev exponent

UR - http://eudml.org/doc/90713

ER -

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