# How can I solve this nonlinear system with 3 equations and 3 unknown? [closed]

I have this system with 3 equations and 3 unknowns:

eqs = {q*(q - a) + u*(-r + 1) (p^r) (j^g)*(b - q) +
r*s*u*(p^(-r - 1)) (j^g) (b - q) == 0,
p*(2*q - a) - u*(p^(-r - 1)) (j^g) + (b - q) (s - b) +
s*u*(p^(-r)) (j^g) - s (b - 2*q) - c*(b - a) == 0,
u*(p^(-r)) g (j^(g - 1))*(b - q) -
s*u*g*(p^(-r)) (j^(g - 1)) (b - q) - (b - a) == 0}


The unknown variables are {p, q, j}.

How can I solve this system, given that

Solve[{q*(q - a) + u*(-r + 1)*(p^r)*(j^g)*(b - q) +
r*s*u*(p^(-r - 1))*(j^g)*(b - q) == 0,
p*(2*q - a) - u*(p^(-r - 1))*(j^g) + (b - q)*(s - b) +
s*u*(p^(-r))*(j^g) - s*(b - 2*q) - c*(b - a) == 0,
u*(p^(-r))*g*(j^(g - 1))*(b - q) -
s*u*g*(p^(-r))*(j^(g - 1))*(b - q) - (b - a) == 0
}, {p, q, j}]


doesn't seem to work?

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The syntax is Solve[eqs,{p,q,j}], but it seems too hard as it stands. Do you have further restrictions like g being integer or alike? –  Rolf Mertig May 3 '13 at 7:06
You appear to be using Matlab functions instead of Mathematica functions. Which system are you using? –  Jonathan Shock May 3 '13 at 7:39
no , unfortunately I haven't got any information about "r" and "g" and "u" ... –  Rozita May 3 '13 at 7:40
If Matlab can solve this system , please tell me , which function or code I should use . –  Rozita May 3 '13 at 7:42
Are you using Mathematica? –  cormullion May 3 '13 at 7:46
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## closed as too localized by belisarius, Sjoerd C. de Vries, m_goldberg, Silvia, Yves KlettMay 6 '13 at 9:08

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## 1 Answer

If you specify some integer value for g and r then you get the solution for your system

  LE[g_, r_] := Module[{eqs},

eqs = {q*(q - a) + u*(-r + 1) (p^r) (j^g)*(b - q) +
r*s*u*(p^(-r - 1)) (j^g) (b - q) == 0,
p*(2*q - a) - u*(p^(-r - 1)) (j^g) + (b - q) (s - b) +
s*u*(p^(-r)) (j^g) - s (b - 2*q) - c*(b - a) == 0,
u*(p^(-r)) g (j^(g - 1))*(b - q) -
s*u*g*(p^(-r)) (j^(g - 1)) (b - q) - (b - a) == 0};
Solve[eqs, {p, q, j}]
]


Like for example

 LE[1,0]


But for higher values of g and r it is taking a lot of time and $mma$ ends up saying "A very large output is generated.."

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Thanks a lot for your attention ... If I change my model to the uniform distribution , I think the equations become easier. But I don't know which code I should use ... –  Rozita May 3 '13 at 13:50
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