# Questions tagged [nonlinear-analysis]

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

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### Confusion about the arrival space of a multivalued operator

I have some confusion about the multivalued operator. Let $X$ Hilbert space. In some books, we find "$A:X\rightarrow 2^{X}$ is an operator." where $2^{X}$ is all subsets of set X. I ...
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### Multivalued and single valued operator

let X Hilbert space et $A:D(A)\subset X \rightarrow 2^{X}$ multivalued nonlinear operator. The Cauchy problem is given by: \begin{eqnarray} U_t(t)+AU(t)&\in&f(t) \;t \in [0,T]\\ U(0)&=&...
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### Global Existence

let X Hilbert space et $A:D(A)\subset X \rightarrow X$ non linear operator. The Cauchy problem is given by: \begin{eqnarray} U_t(t)+AU(t)&=&f(t) \;t \in [0,T]\\ U(0)&=&U_0 \end{...
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### How to show sin(f(t) where $f(t)) \in L^2(0,1)$ is lipschitz continuous?

How to show sin(f(t)) where $f(t) \in L^2(0,1)$ is Lipchitz continuous? sin(f(t)) is a mapping from $L^2(0,1) \to L^2(0,1)$. I was surprised that this composition is even continuous in the first place....
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### Existence of global solutions to a Bernoulli differential equation/inequality

I'm looking at some Bernoulli type differential equations at the moment and came across another question: First order nonlinear differential inequality. This got me thinking that the Bernoulli ...
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### A condition on a fifth order differential equation

This may be very obvious but I am stuck trying to solve a boundary value problem. I am trying to solve the following differential equation : $$F^{3}F^{(5)}+F=1 \space (Eq.1)$$ I have been advised to ...
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### Can $f_1(x, y)-f_2(u, v)$ be written as $g(x-u, y-v)$?

when I do some calculation on the basic theory of diffractive neural networks,the question behind blocks my way.It's a pure math that i want to know, $f_1 (x, y)$ and $f_2(u, v)$ are both nonlinear ...
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### Show u^2|u|^(p-3) is Holder continuous (derivative of power nonlinearity)

I am trying to show that the function $f:\mathbb{C}\rightarrow \mathbb{C}$ given by $f(u)=u^2|u|^{p-3}$ is (uniformly) Holder continuous for $p\in(1,2)$ (so $p-3\in(-2,-1)$, this ensures that $f$ is ...
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### How can I find closed loop dynamics of this system?

There is controller, where $a>0$. Now, if $v>0$, then $u = \ddot\theta(t)$ and if $v<0$, then $-u=\ddot\theta(t)$. However, how can I detect whether $v$ is positive or negative?
Let a function $f:X\rightarrow \mathbb{R}^n$, where $X \subseteq \mathbb{R}^n$, satisfy the Lipschitz continuity condition $$\|f(x) - f(y) \| \leq L \|x-y\|, \quad \forall x,y\in X$$ where $L\geq 0$ ...