- #1
timo1023
- 8
- 0
Hello,
I have the 2nd-order nonlinear ODE below:
[tex]
k(v)=\frac{\phi ''(v)}{\phi (v) (\phi ' ^2 (v) +1)^2}
[/tex]
Where k(v) is some function. I would like to investigate for what functions k there can exist solutions on a given interval [tex][a,b][/tex]. For example, if [tex]k(v)=0[/tex], then [tex]\phi '' (v)=0[/tex] which implies that [tex]\phi (v)=C_1 v + C_2[/tex]. The DE gets very complicated very quickly, though, and I'm not sure how to approach the problem.
I do not know very much about differential equations, so I need help in figuring out what to learn. What are the methods for analyzing such a DE? Are there any existence theorems or uniqueness theorems already out there? Can anyone recommend some good literature?
Thanks for the help.
I have the 2nd-order nonlinear ODE below:
[tex]
k(v)=\frac{\phi ''(v)}{\phi (v) (\phi ' ^2 (v) +1)^2}
[/tex]
Where k(v) is some function. I would like to investigate for what functions k there can exist solutions on a given interval [tex][a,b][/tex]. For example, if [tex]k(v)=0[/tex], then [tex]\phi '' (v)=0[/tex] which implies that [tex]\phi (v)=C_1 v + C_2[/tex]. The DE gets very complicated very quickly, though, and I'm not sure how to approach the problem.
I do not know very much about differential equations, so I need help in figuring out what to learn. What are the methods for analyzing such a DE? Are there any existence theorems or uniqueness theorems already out there? Can anyone recommend some good literature?
Thanks for the help.