Second-order elliptic differential inequalities in Banach spaces

Authors:
Gerd Herzog;Roland Lemmert
Affiliations:
Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany;Mathematisches Institut I, Universität Karlsruhe, D-76128 Karlsruhe, Germany
Venue:
Nonlinear Analysis: Theory, Methods & Applications
Year:
2003

Citing 2
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nonlinear elliptic boundary-value problems in unbounded domains

Nonlinear Analysis: Theory, Methods & Applications
Ordinary Differential Equations

Ordinary Differential Equations

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Abstract

We derive monotonicity results for solutions of partial differential inequalities (of elliptic type) in ordered normed spaces with respect to the boundary values. As a consequence, we get an existence theorem for the Dirichlet boundary value problem by means of a variant of Tarski's fixed point theorem.