# Questions tagged [nonlinear-analysis]

For questions on nonlinear analysis, a branch of mathematical analysis that deals with nonlinear mappings.

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### How to add nonlinear function to equation without transformed output

I am trying to adjust an equation to account for a non-linear trend, while preserving the final product without a transformation. My target, is to estimate a concentration gradient, e.g. If the air ...
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### solving first order nonlinear equation [closed]

I need to solve this equation n`(t)=co I(t)+ c1 n(t)+ c2 n^2(t) +c3 n^3(t) by hand analysis not computer programs. what other methods than Euler's method? Thank you
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### possible structure for the optimal solution

Consider the following problem $$\max_{x_{ij} \in [0, 1]} \sum\limits_{i=1}^n\sum\limits_{j=1}^n c_{ij} f_{ij}(x_{ij}) \frac{g_i(x)}{\max(g_1(x), g_2(x), \cdots, g_n(x))},$$ where $f_{ij}$ is a ...
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### What does the non-existence of Lyapunov number mean? [closed]

For discrete dynamical system, $\mathbf{F}:\mathbb{R}^m\rightarrow\mathbb{R}^m$, $k$-th Lyapunov number of the orbit beginning from $\mathbf{x}_0\in \mathbb{R}^m$ is defined as follow. \begin{align} \...
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1answer
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### Is the sine operator on $L^2[0,1]$ Fréchet differentiable or not and why?

This problem has given me some trouble. Let $F$ be the operator on $L^2[0,1]$ defined by $F(g)(t)=\sin g(t)$. I'm trying to determine whether or not $F$ is (Fréchet) differentiable in that space. I ...
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### How to find a quadratic convergence function on fixed point iteration method on root finding?

I've read several references, and it is true that: A point is called a fixed point if $f(x_0) = x_0$. It can further be reduced to find root of a non-linear function $f(x) = g(x) - x = 0$ The fixed ...
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1answer
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### On continuity of the Gateaux derivative of p-Laplacian operator

Let $\Omega\subset \mathbb{R}^n, N\geq3$, be an open set. For $p\in(1,+\infty)$, define a functional $J:W_0^{1,p}(\Omega)\rightarrow\mathbb{R}$ by $J(u)=\int_\Omega |\nabla u|^p\,dx.$ Then $J$ is ...
1answer
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### Obtain non linear solution using neural network

The function f(x)=theta·x where theta is a row vector and x is a column vector, is a linear function. How can I obtain a non-linear function g(x) using a multi layer network, that also takes in x as ...
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### How to do a 3 constant reciprocal (multiplicative inverse) regression

I am trying to fit a set of data to a curve such as: $y=\frac{m}{x-a}+b$ Without the constant $a$, it is easy to define $z=\frac{1}{x}$ and convert it to a linear model. But I have not been able to ...
1answer
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### Non-linear function with properties related to Gaussian distribution

Let $\mathcal{A}_n$ be the set of functions $f : \mathbb{R} \to \mathbb{R}^n$ such that: $f$ is continuous and $f$ is differentiable almost everywhere if $X \sim \mathcal{N}(0, 1)$, then: \$E[f(X)] = ...