<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">MOHAMED  EL-GEBEILY</style></author><author><style face="normal" font="default" size="100%">DONAL O’REGAN</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">EXISTENCE AND QUASILINEARIZATION FOR A CLASS OF NONLINEAR ELLIPTIC SECOND ORDER PARTIAL DIFFERENTIAL EQUATIONS</style></title><secondary-title><style face="normal" font="default" size="100%">Dynamic Systems and Applications</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">41A65</style></keyword><keyword><style  face="normal" font="default" size="100%">47J05</style></keyword><keyword><style  face="normal" font="default" size="100%">47J25</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://acadsol.eu/dsa/articles/17/DSA-2007-445-458.pdf</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">17</style></volume><pages><style face="normal" font="default" size="100%">14</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;In this paper we discuss some existence results and the application of quasilinearization methods to the solution of second order nonlinear self adjoint elliptic partial differential equation in R&lt;sup&gt;n&lt;/sup&gt; with Dirichlet boundary conditions. Under fairly general assumptions on the data of the problem we show the existence of a solution that can be obtained as the limit of a quadratically convergent nondecreasing sequence of approximate solutions. If the assumptions are strengthened, we show that the solution can be quadratically bracketed between two monotone sequences of approximate solutions of certain related linear equations.&lt;/p&gt;
</style></abstract><section><style face="normal" font="default" size="100%">445</style></section></record></records></xml>