Extremal solutions for nonlinear neumann problems

Antonella Fiacca; Raffaella Servadei

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2001)

  • Volume: 21, Issue: 2, page 191-206
  • ISSN: 1509-9407

Abstract

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In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.

How to cite

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Antonella Fiacca, and Raffaella Servadei. "Extremal solutions for nonlinear neumann problems." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 21.2 (2001): 191-206. <http://eudml.org/doc/271451>.

@article{AntonellaFiacca2001,
abstract = {In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.},
author = {Antonella Fiacca, Raffaella Servadei},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {upper solution; lower solution; order interval; truncation function; penalty function; pseudomonotone operator; coercive operator; extremal solution; nonlinear Neumann problem; -Laplacian},
language = {eng},
number = {2},
pages = {191-206},
title = {Extremal solutions for nonlinear neumann problems},
url = {http://eudml.org/doc/271451},
volume = {21},
year = {2001},
}

TY - JOUR
AU - Antonella Fiacca
AU - Raffaella Servadei
TI - Extremal solutions for nonlinear neumann problems
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2001
VL - 21
IS - 2
SP - 191
EP - 206
AB - In this paper, we study a nonlinear Neumann problem. Assuming the existence of an upper and a lower solution, we prove the existence of a least and a greatest solution between them. Our approach uses the theory of operators of monotone type together with truncation and penalization techniques.
LA - eng
KW - upper solution; lower solution; order interval; truncation function; penalty function; pseudomonotone operator; coercive operator; extremal solution; nonlinear Neumann problem; -Laplacian
UR - http://eudml.org/doc/271451
ER -

References

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  14. [14] J. Leray and J.L. Lions, Quelques Resultats de Visik sur les Problems Elliptiques Nonlinearities par Methodes de Minty-Browder, Bull. Soc. Math. France 93 (1965), 97-107. Zbl0132.10502
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