# Tagged Questions

Ordinary or partial differential equations. Delay differential equations, neutral equations, integro-differential equations. Well-posedness, asymptotic behavior, and related questions.

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### Modifying monkey saddles

We get negative Gauss curvature K surfaces of quasi polar symmetry surface form generated from: $$Re (x+ i y)^n = a^n$$ (n integer) with n humps above plane $z =0$. ($n =2,3,4$ hyperbolic ...
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### Noninvariance for a specific nonlinear oscillator

Consider the nonlinear system \begin{align*} \frac{d}{dt} \begin{pmatrix} x_1(t) \\ x_2(t) \end{pmatrix} = \begin{pmatrix} x_2(t) \\ -4x_1(t) + x_1^2(t) \end{pmatrix}, \end{align*} which admits ...
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### Method of characteristics [closed]

I have difficulties understanding how to solve a PDE in $\mathbb{R}^{4}$ using the method of characteristics. I have a limited background in solving PDEs. I have seen only 2-dim examples and none for ...
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### The complex leaves containing real limit cycles of Lienard equation

According to the answer and comments to this question we realize that a useful approach to such type of questions is to consider algebraic vector field which possess algebraic solutions. On the ...
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### Two limit cycles which lie on the same leaf

Edit 1: For a related discussion see this MSE post I apologize in advance, if this question is obvious: 1)What is an example of a polynomial vector field on $\mathbb{R}^{2}$ with at least two ...
Is there a polynomial Hamiltonian $H:\mathbb{R}^{4}\to \mathbb{R}$ such that the number of nontrivial periodic orbits of the corresponding Hamiltonian vector field $X_{H}$ is finite but different ...
### Given $x$ in a path-connected open set $S$ on the plane, are there non-crossing paths from $x$ to every point in $\partial S$?
A have a (non-simply) bounded path-connected open set $S\subset\mathbb{R}^2$. Given $x\in S$, there are paths in $S$ from $x$ to any point in the boundary $\partial S$. However, can all these paths ...