Advanced Calculus: The Existence Theorem for Nonlinear Differential Equations
Not what you're looking for?
Please see the attached file for the fully formatted problems.
Let g(x,y) be Lipschitz continuous. Let ? (x) = y , and for n > 0 define ? (x) = y +
Prove that ? (x)  ?(x) on [x - , x + ], for some > 0, where ?(x) solves the ODE ?'(x) = g(x, ?(x)), and ?(x ) = y
Purchase this Solution
Solution Summary
The existence theorem for nonlinear differential equations is discussed.
Solution Preview
Please see the attached file for the complete solution.
Thanks for using BrainMass.
Proof:
is Lipschitz continuous, then it satisfies the Lipschitz condition. There exists , such that is continuous, so we can suppose is continous in a rectangular region , . Since is a closed region, can reach its maximum value in this ...
Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems
Understanding of how geometry applies to in real-world contexts
Solving quadratic inequalities
This quiz test you on how well you are familiar with solving quadratic inequalities.
Know Your Linear Equations
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Probability Quiz
Some questions on probability
Graphs and Functions
This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.