Questions tagged [nonlinear-analysis]

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

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Variable coefficient differential equation

I am absolutely not familiar with differential equations. However, I am facing the following differential equation: $$a(x)y^{\prime}(x)+b(x)y(x)=c(x)\sqrt{1-d(x)y^{2}(x)}$$ ...
• 183
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Solving Abel equation of the second kind

I am absolutely not familiar with differential equations. However, I am facing the following non-linear variable coefficient ordinary differential equation: a(x)y^{3}(x) + b(x)y^{2}(x)...
• 183
1 vote
35 views

How to accurately average a function with a nonlinear response?

I am a physics PhD student working in optics and I have a bit of a weird problem that I am trying to sort out and I'm hoping you math folks can help me with. Without boring you with the experimental ...
45 views

Holomorphic implicit function theorem

Is there a version of the implicit function theorem for holomorphic functions between complex Banach spaces? If yes, do you know any reference?
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Does the presence of neural bias change the hypothesis space of a NN?

This question has to do with neural networks, but it is a purely mathematical question, so I think it belongs here. Consider $f: \mathbb{R}^N \to \mathbb{R}^M$ such as to be implementable with a ...
• 363
19 views

Extension of degree theory on sub-manifolds to manifolds

I am learning the Brouwer degree in the settings of sub-manifolds sztisfying hood assumptions (compactness, orientation, connectedness). I would like to know if there is a reasonable way to extend it ...
• 1,381
1 vote
43 views

normalizable solution of a nonlinear equation

How to find a normalizable solution of the nonlinear differential equation below? $$R'' + \frac{R'}{r} - R + R^3 =0 .$$ The domain is $[0,\infty ]$ and we want the norm of the solution to be ...
• 1,015
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Volterra integral operator is completly continuous, given that its kernel is continuous

Prove that Volterra integral operator on $C[a,b]$ is completly continuous, knowing its kernel $K:C[a,b]\times[a,b]\times\mathbb{R}\rightarrow\mathbb{R}$ is continuous. I used this definition, the ...
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1 vote
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How is it OK to safely neglect one-step difference of the system state in this paper?

I’m reading a very informative paper. But I met some formulations hard to understand. In assumption 2, they have the inequality of one step difference, \Delta u_k \leq \sigma(B_o^{-1})\big(L_a\Delta ...
• 165
I'm reading a very informative paper. But I met some formulations hard to accept. In the stability proof section (Sec. V, Theorem 5.2), they define a Lyapunov function as $V(s) = \frac{1}{2}m\|s\|^2$ ...