MATLAB: How to i find a range of parameters that admit positive solutions

nonlinearsymbolic

Hi,
I have this non linear equation.
x+6-(beta/(1+beta))*(1-alpha)*x^(alpha)+(exp(sigma^2*(1/2 - x/((beta/(1+beta))*(1-alpha)*x^(alpha)))))*((beta/(1+beta))*alpha*x^(2*alpha-1)-(alpha)*x^(alpha))=0
my alpha's, beta's and sigma, are parameters. I am wondering how someone can find in MATLAB the range or value/values of those parameters that admit positive solution/s for my x.
Thanks

Best Answer

Here is a combination of parameters that seems to satisfy your equation, with x>=0,
alpha =
     -0.0786
beta =
      1.8827
x =
      0.2446
sigma =
      4.2678
I obtained it by minimizing abs(LHS) over all 4 parameters via the code below.
    LHS=@(alpha,beta,x,sigma) x+6-(beta/(1+beta))*(1-alpha)*x^(alpha)+(exp(sigma^2*(1/2 - x/((beta/(1+beta))*(1-alpha)*x^(alpha)))))*((beta/(1+beta))*alpha*x^(2*alpha-1)-(alpha)*x^(alpha));
      fun=@(p) abs(LHS(p(1),p(2),abs(p(3)),p(4)));
      options=optimset('TolFun',1e-6);
      [p,fval]=fminsearch(fun,[1,1,1,3],options);
      alpha=p(1),
      beta=p(2),
      x=abs(p(3)),
      sigma=abs(p(4)),
So does this complete your mission?
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