# Sous-Solutions de Problèmes aux Limites en Dimension 1

Sous-Solutions de Problèmes aux Limites en Dimension 1 We consider a boundary value problem $$- v = {\text{f , }}v \in \phi (u){\text{ }}on]0,1[ E(v\left( 0 \right),v\left( 1 \right)) \mathrel\backepsilon (v\prime \left( 0 \right),\user1{ - }v\prime \left( 1 \right))$$ where ϕ is a maximal monotone operator in ℝ and E is a multivalued operator in ℝ2 with non decre asing resolvent. We introduce a condition on E which insures that the operator inL 1 (0,1) associated to this problem has non decreasing resolvent, and caracterise the subsolutions of the problem. We give different examples of operatorsE satisfying this condition. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

# Sous-Solutions de Problèmes aux Limites en Dimension 1

, Volume 1 (2) – Oct 14, 2004
19 pages

/lp/springer_journal/sous-solutions-de-probl-mes-aux-limites-en-dimension-1-NuRiuW0mHU
Publisher
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1023/A:1009786324575
Publisher site
See Article on Publisher Site

### Abstract

We consider a boundary value problem $$- v = {\text{f , }}v \in \phi (u){\text{ }}on]0,1[ E(v\left( 0 \right),v\left( 1 \right)) \mathrel\backepsilon (v\prime \left( 0 \right),\user1{ - }v\prime \left( 1 \right))$$ where ϕ is a maximal monotone operator in ℝ and E is a multivalued operator in ℝ2 with non decre asing resolvent. We introduce a condition on E which insures that the operator inL 1 (0,1) associated to this problem has non decreasing resolvent, and caracterise the subsolutions of the problem. We give different examples of operatorsE satisfying this condition.

### Journal

PositivitySpringer Journals

Published: Oct 14, 2004

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