my function was written incorrectly, this runs without problem and finds a zero
function R(F,p) #p is a vector too, not a number
F[1] = -5.0488*p[1] + p[1]^2.81 - 3.38/( p[1]^(-1.0) )^2.0
end
nlsolve(R , [5.8])
the results are:
julia> nlsolve(R , [5.8])
Results of Nonlinear Solver Algorithm
* Algorithm: Trust-region with dogleg and autoscaling
* Starting Point: [5.8]
* Zero: [5.934184191445043]
* Inf-norm of residuals: 0.000000
* Iterations: 3
* Convergence: true
* |x - x'| < 0.0e+00: false
* |f(x)| < 1.0e-08: true
* Function Calls (f): 4
* Jacobian Calls (df/dx): 4