## Maximum Principles For Some Differential Inequalities With Applications

Maximum Principles For Some Differential Inequalities With Applications

Mohammad Almahameed

Mohammad Almahameed "Maximum Principles For Some Differential Inequalities With Applications" Published in International Journal of Trend in Research and Development (IJTRD), ISSN: 2394-9333, Special Issue | ICAST-17 , December 2017, URL: http://www.ijtrd.com/papers/IJTRD14633.pdf

In this paper we consider several types of differential equations and discuss the maximum principle for them. In general, the maximum principle tells us that the maximum value of the function, which is a solution of a differential equation, is attained at the boundary of the region. In this paper, we deal with elliptic equations. The most important and easy equation is the Laplace equation. The homogeneous version of Laplace’s equation is ?u = 0. It is often written with minus sign since the (delta-operator) with this sign becomes strict monotone operator in the operator theory, which means that it has a unique solution. The non-homogeneous version of Laplace’s equation ?u = f is called Poisson’s equation. It is convenient to include a minus sign here because ? is a negative definite operator. The Laplace and Poisson equations, and their generalizations, arise in many different contexts. 2010 Math. Subject Classification: 35R45, 35R50

Differential Equations, Maximum principles

Special Issue | ICAST-17 , December 2017

2394-9333

IJTRD14633
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