What is the class of this equation?

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The equation discussed is a 3D second-order non-linear partial differential equation represented as \(\Delta u(\vec{r}) = F(u(\vec{r}), \vec{r})\). There are no established general methods for solving this type of equation due to the arbitrary nature of the right-hand side function \(F\). Participants in the discussion confirm the complexity of finding solutions, emphasizing the lack of a universal approach for such equations.

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Hi all,

Please tell me the class of this equation, and if possible how to solve this kind of equations:

[itex]\Delta[/itex]u([itex]\vec{r}[/itex])=F(u([itex]\vec{r}[/itex]),[itex]\vec{r}[/itex])


Thanks in advance.
 
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3D 2nd order non-linear - no 1st order term.
IIRC: There are no general approaches for solving this type of equation.
The trouble is that the RHS function can be ANYTHING.
 

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