Nonlinear Analysis and Differential Equations
by Klaus Schmitt, Russell C. Thompson
Publisher: University of Utah 2004
Number of pages: 158
The intent of this set of notes is to present several of the important existence theorems for solutions of various types of problems associated with differential equations and provide qualitative and quantitative descriptions of solutions. At the same time, we develop methods of analysis which may be applied to carry out the above and which have applications in many other areas of mathematics, as well.
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by Gerald Teschl - Universitaet Wien
This book provides an introduction to ordinary differential equations and dynamical systems. We start with some simple examples of explicitly solvable equations. Then we prove the fundamental results concerning the initial value problem.
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Some examples of simple differential equations. The book covers separation of variables, linear differential equation of first order, the existence and uniqueness theorem, the Bernoulli differential equation, and the setup of model equations.
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These notes contain various versions of the contraction mapping principle. Several applications to existence theorems in differential and integral equations and variational inequalities are given. Also discussed are Hilbert's projective metric.
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