%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% %%%% %%%% ABSTRACT TEMPLATE FOR THE %%%% %%%% CONFERENCE ON BOUNDARY VALUE PROBLEMS. %%%% %%%% MATHEMATICAL MODELS IN ENGINEERING, BIOLOGY AND MEDICINE. %%%% %%%% September 16-19, 2008, Santiago de Compostela, Spain %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% %%%% %%%% PLEASE SAVE THE FILE AS BVP-Surname of the speaker.tex %%%% %%%% VERIFY THAT THE LENGTH OF PDF FILE DOES NOT EXCEED ONE PAGE %%%% %%%% AND SEND BOTH FILES TO THE E-MAIL: bvp2008@gmail.com %%%% %%%% WITH THE SUBJECT: ABSTRACT-BVP %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% %%%% %%%% PLEASE DO NOT USE ANY ADDITIONAL PACKAGES, DEFINE ANY MACROS OR %%%% %%%% MAKE ANY ALTERATIONS TO LINES BELOW THAT FINISH WITH %* %%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%* \documentclass{article} %* \usepackage{latexsym} %* \usepackage{amsmath,amsthm,amsfonts} %* \usepackage{amssymb} %* \usepackage{palatino} %* \usepackage[mathscr]{eucal} %* \textwidth 16cm \textheight 26cm \oddsidemargin 0cm \evensidemargin %* 0cm \topskip 0cm \headheight 0cm \topmargin 0cm \pagestyle{empty} %* \allowdisplaybreaks %* \newcommand{\head}{{\noindent \small Mathematical Models in Engineering, %* Biology and Medicine. \\ Conference on Boundary Value Problems.\\ %* September 16-19, 2008, Santiago de Compostela, Spain.} \vspace{7pt}} %* \newcommand{\inserttitle}[1]{\begin{center}{\Large\bf #1}\end{center}} %* \newcommand{\insertauthor}[1]{\begin{center}{\sc #1}\end{center}} %* \begin{document} %* \parindent 0mm %* \pagestyle{empty} %* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%* %*************** PLEASE DO NOT REMOVE THIS STAR LINE ***************************************** \newpage %* \thispagestyle{empty} %* \vspace*{-2cm} %* \head %* \bigskip %* %%%%% INSERT HERE THE TITLE %%%%%%%%%%%%%%%%%%%%%%* \inserttitle{Nonlinear singular differential equations with nonlinear functional conditions} \vspace{0.5cm} %* %%%% UNDERLINE THE NAME OF THE SPEAKER %%%%%%%%%%%%* \insertauthor{\underline{Alberto Cabada} and Jos\'e \'Angel Cid} \vspace{0.5cm} %* \textbf{Keywords:} {\it Singular equations, nonlinear boundary conditions.} \textbf{MSC2000 Classification:} 34B15, 34B16. %%%%%%%%%%% INSERT HERE THE ABSTRACT %%%%%%%%%%%%%* \vspace{0.75cm} %* \begin{center} {\large\bf Abstract} \end{center} %* Equations of the form $$(k(u(t))u'(t))'=f(t,u(t)),$$ coupled with different types of boundary value conditions model several diffusion problems as semiconductor fabrication, infiltration of water from reservoirs and the problem of the diffusion of a dopant throught a semiconductor [3, 4]. Some recent papers have considered different variations of this equation, obtaining existence results by assuming weaker regularity conditions in the function $k$ (see [2]). \par Recently in [1] we consider the equation $$-(k(t,u(t))u'(t))'=f(t,u(t)) \quad \mbox{for a. a. } t \in [0,1],$$ subject to different kinds of nonlinear functional boundary conditions which include, among others, the Dirichlet and multipoint boundary value conditions as a particular cases. We allow $k(0,x)$ or $k(1,x)$ vanish at some real values $x$ and, as a consequence, we are dealing with singular equations. \par Assuming the existence of a pair of lower and upper solutions with "corners" we prove the existence of at least one solution lying between them. %%%%%%%%%%%%%% INSERT HERE THE REFERENCES %%%%%%%%%%* \vspace{0.5cm} {\large \bf References}\\ \begin{itemize} \item[{[1]}] {A. Cabada and J. A. Cid,} Existence of solution for a singular differential equation with nonlinear functional boundary conditions, {\it Glasg. Math. J.} {\bf 49}, (2007), 2, 213 -- 224. \item[{[2]}] {A. Cabada, J. A. Cid and R. L. Pouso,} Positive solutions for a class of singular differential equations arising in diffusion processes, {\it Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.} {\bf 12}, (2005), 3 -- 4, 329 -- 342. \item[{[3]}] {S. It$\hat{\mbox{o}}$}, {\em Diffusion equations}, Translations of Mathematical Monographs, {\bf 144}, A.M.S., Providence, Rhode Island, 1992. \item[{[4]}] {W. Okrasinski,} {On approximate solutions to some nonlinear diffusion problems,} {\it Z. Angew. Math. Phys.} {\bf 44}, (1993), 4, 722 -- 731. \end{itemize} %%%%% INSERT HERE THE COMPLETE ADDRESSES OF THE AUTHORS %%%%%%%%%* \vspace{0.75cm} %* \footnotesize{Alberto Cabada \\ University of Santiago de Compostela, Department of Mathematical Analysis, Santiago de Compostela, Galicia, Spain.\\ e-mail: cabada@usc.es \\ Webpage: http://web.usc.es/$\sim$cabada \\} \vspace{0.25cm} \footnotesize{Jos\'e \'Angel Cid \\ University of Ja\'en, Department of Mathematics, Campus Las Lagunillas, Ja\'en, Spain.\\ e-mail: angelcid@ujaen.es \\} %*************** PLEASE DO NOT REMOVE THIS STAR LINE ***************************************** \end{document} %*