For questions on nonlinear analysis, a branch of mathematical analysis that deals with nonlinear mappings.
Questions tagged [nonlinear-analysis]
533 questions
2
votes
0 answers
Nonlinear frequency shift
I came across the following equation:
$\frac{dz}{dt}+iz=iεxy^{2}$, t is a dimensionless time, $z=x+\frac{idx}{dt}$, $y=\frac{dx}{dt}$. I would like to find a nonlinear frequency shift. I tried to decompose the right part by composing only resonant…
MaximBr
- 21
2
votes
1 answer
proving the stability of the equilibrium point with a Lyapunov function
The below nonlinear system is considered as a pendulum with a nonlinear damping coefficient:
$$
\ddot y+(a+b\cos(y))\dot y+c\sin(y)=0, \qquad a\geq b\geq 0
$$
Use the energy of the whole system as a Lyapunov function to check the stability of the…
user212662
- 33
1
vote
1 answer
One-phase association fit / rate constant value comparison
Currently, I am writing my thesis (in molecular biology - not mathematics), and I am puzzled over the results.
I measured an increase in a signal and did a one-phase association fit in GraphPad. Now, I have four curves, and they look as we would…
cmp4
- 11
- 2
1
vote
0 answers
Solving a super-quadric equation
I have to solve the following scalar non-linear equation.
\begin{equation*}
\xi^{\frac{2}{\varepsilon}}+(\xi-k)^{\frac{2}{\varepsilon}}=1
\end{equation*}
with respect to $\xi\geq 0$. Here $\varepsilon>0$ and $k\in[0,1]$ are given parameters. So far…
matteogost
- 677
1
vote
0 answers
A question about homeomorphisms of Banach space
Let $X$ be an Banach space and let $g:X \to X$ be a map such that:
1) $g$ is non linear and compact (i.e. if $B$ is a bounded subset of $X$ then $g(B)$ is a precompact subset of $X$)
2) the function $f:=id+g : X \to X$, is a global homeomorphism…
stefano
- 11
0
votes
0 answers
Growth conditions for elliptic quasilinear equations in divergence form
Let us consider the following elliptic quasilinear problem with mixed
boundary conditions
$$
\left.\begin{alignedat}{2}-\textrm{div}[a(x,u,\nabla u)]+c(x,u,\nabla u) & =g & & \textrm{in}\,\Omega\\
\nu\cdot a(x,u,\nabla u)+b(x,u) & =h & &…
RiemannGauss
- 199
0
votes
2 answers
How to make small values matter in a non-linear regression analysis
I have a dataset with some of the following values:
independent variable n: dependent variable t
196: 8.32E-05
676: 0.000360012
..: ..
2739025: 17.19871902
4422609: 34.82757854
I am trying to match this empirical data to the closest…
0
votes
1 answer
Approach to solving underdetermined nonlinear system of equations
I've gotten into a problem I haven't really worked with before in my numerics classes.
I have a system of four nonlinear equations with six parameters.
Newtons method, Boydens method etc. all include the inverse of the jacobian, but if the system…
1233023
- 543
0
votes
0 answers
Want least squares estimates of nonlinear model and its variances.
The problems is
Suppose that E(Y_i|X)=$\beta_0+\beta_1\sin(2 \pi \theta_1 i/n)+\beta_2\cos(2\pi\theta_2i/n)$, i=1,...n, where positive integers $\theta_1$ and $\theta_2 $ are given.
I want to find least squares estimates of…
GGyu
- 1
0
votes
1 answer
How do I solve this nonlinear equation using lambert w function?
I have been trying to solve this nonlinear equation for sometime now to no avail. I have tried Mathematica and matlab as well. But I believe that a solution exist in terms of x (probably using the Lambert W function).
This is the equation…
-1
votes
1 answer
Nonlinear equation $6 + \sinh(x) = \sinh(3x)$
I have this equation
$6 + \sinh(x) = \sinh(3x)$
I know that I have to use this equation
$\sinh(3x) = 3\sinh(x) + 4\sinh^3(x)$
and substitution
Can anybody please help me? thx
naruto25
- 461