The Neumann problem for quasilinear differential equations

Tiziana Cardinali; Nikolaos S. Papageorgiou; Raffaella Servadei

Archivum Mathematicum (2004)

  • Volume: 040, Issue: 4, page 321-333
  • ISSN: 0044-8753

Abstract

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In this note we prove the existence of extremal solutions of the quasilinear Neumann problem - ( | x ' ( t ) | p - 2 x ' ( t ) ) ' = f ( t , x ( t ) , x ' ( t ) ) , a.e. on T , x ' ( 0 ) = x ' ( b ) = 0 , 2 ≤ p < ∞ in the order interval [ ψ , ϕ ] , where ψ and ϕ are respectively a lower and an upper solution of the Neumann problem.

How to cite

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Cardinali, Tiziana, Papageorgiou, Nikolaos S., and Servadei, Raffaella. "The Neumann problem for quasilinear differential equations." Archivum Mathematicum 040.4 (2004): 321-333. <http://eudml.org/doc/249284>.

@article{Cardinali2004,
abstract = {In this note we prove the existence of extremal solutions of the quasilinear Neumann problem $-( \vert x^\{^\{\prime \}\}(t) \vert ^\{p-2\}x^\{^\{\prime \}\}(t))^\{^\{\prime \}\} = f(t,x(t),x ^\{^\{\prime \}\}(t))$, a.e. on $T$, $x^\{^\{\prime \}\}(0) = x^\{^\{\prime \}\}(b) =0$, $2\le p < \infty $ in the order interval $[\psi ,\varphi ]$, where $\psi $ and $\varphi $ are respectively a lower and an upper solution of the Neumann problem.},
author = {Cardinali, Tiziana, Papageorgiou, Nikolaos S., Servadei, Raffaella},
journal = {Archivum Mathematicum},
keywords = {upper solution; lower solution; order interval; truncation function; penalty function; pseudomonotone operator; coercive operator; Leray-Schauder principle; maximal solution; minimal solution; upper solution; lower solution; order interval; truncation function},
language = {eng},
number = {4},
pages = {321-333},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {The Neumann problem for quasilinear differential equations},
url = {http://eudml.org/doc/249284},
volume = {040},
year = {2004},
}

TY - JOUR
AU - Cardinali, Tiziana
AU - Papageorgiou, Nikolaos S.
AU - Servadei, Raffaella
TI - The Neumann problem for quasilinear differential equations
JO - Archivum Mathematicum
PY - 2004
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 040
IS - 4
SP - 321
EP - 333
AB - In this note we prove the existence of extremal solutions of the quasilinear Neumann problem $-( \vert x^{^{\prime }}(t) \vert ^{p-2}x^{^{\prime }}(t))^{^{\prime }} = f(t,x(t),x ^{^{\prime }}(t))$, a.e. on $T$, $x^{^{\prime }}(0) = x^{^{\prime }}(b) =0$, $2\le p < \infty $ in the order interval $[\psi ,\varphi ]$, where $\psi $ and $\varphi $ are respectively a lower and an upper solution of the Neumann problem.
LA - eng
KW - upper solution; lower solution; order interval; truncation function; penalty function; pseudomonotone operator; coercive operator; Leray-Schauder principle; maximal solution; minimal solution; upper solution; lower solution; order interval; truncation function
UR - http://eudml.org/doc/249284
ER -

References

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