# An elliptic equation with no monotonicity condition on the nonlinearity

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 4, page 786-794
- ISSN: 1292-8119

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topSpradlin, Gregory S.. "An elliptic equation with no monotonicity condition on the nonlinearity." ESAIM: Control, Optimisation and Calculus of Variations 12.4 (2006): 786-794. <http://eudml.org/doc/249614>.

@article{Spradlin2006,

abstract = {
An elliptic PDE is studied which is a perturbation of an autonomous
equation. The existence of a nontrivial solution is proven via
variational methods. The domain of the equation is unbounded, which
imposes a lack of compactness on the variational problem. In addition,
a popular monotonicity condition on the nonlinearity is not assumed. In
an earlier paper with this assumption, a solution was obtained using a
simple application of topological (Brouwer) degree. Here, a more subtle
degree theory argument must be used.
},

author = {Spradlin, Gregory S.},

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

keywords = {Mountain-pass theorem; variational methods; Nehari manifold;
Brouwer degree; concentration-compactness.; Brouwer degree; concentration-compactness},

language = {eng},

month = {10},

number = {4},

pages = {786-794},

publisher = {EDP Sciences},

title = {An elliptic equation with no monotonicity condition on the nonlinearity},

url = {http://eudml.org/doc/249614},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Spradlin, Gregory S.

TI - An elliptic equation with no monotonicity condition on the nonlinearity

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/10//

PB - EDP Sciences

VL - 12

IS - 4

SP - 786

EP - 794

AB -
An elliptic PDE is studied which is a perturbation of an autonomous
equation. The existence of a nontrivial solution is proven via
variational methods. The domain of the equation is unbounded, which
imposes a lack of compactness on the variational problem. In addition,
a popular monotonicity condition on the nonlinearity is not assumed. In
an earlier paper with this assumption, a solution was obtained using a
simple application of topological (Brouwer) degree. Here, a more subtle
degree theory argument must be used.

LA - eng

KW - Mountain-pass theorem; variational methods; Nehari manifold;
Brouwer degree; concentration-compactness.; Brouwer degree; concentration-compactness

UR - http://eudml.org/doc/249614

ER -

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