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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6410 • ODE

Fall 1996 • Question 2

Question

Math 6410 • ODE Fall 1996 • Question 2

Define \[ f:E\to X \] by \[ u\mapsto f(u)=u''+\lambda u+u^3, \tag {2.1} \] where \(\lambda \in \mathbb {R}\). Show that \(f\) is a \(C^1\) mapping.

Raw LaTeX

Define
\[
f:E\to X
\]
by
\[
u\mapsto f(u)=u''+\lambda u+u^3,
\tag{2.1}
\]
where \(\lambda\in\R\). Show that \(f\) is a \(C^1\) mapping.

Topic Tags

Contraction Mapping and Nonlinear Equations