# Finding good boundary conditions NDSolveValue

I have the following differential equation to solve :

a = 3/4
e = 0.000000001
P[x_] = -x^2 + a*x^4
P1[x_] = P'[x]
P2[x_] = P''[x]
l = 0.5
xmax = 1
sol = NDSolveValue[{Div[f[x]*(1 - f[x])* Grad[P1[f[x]] -
0.01*Laplacian[f[x], {x, y, z}, "Spherical"], {x, y, z},
"Spherical"], {x, y, z}, "Spherical"] == 0,
f[xmax] == 2/3, f'[e] == e, f'''[e] == e, f''[e] == e}, f, {x, e, xmax}]

but Mathematica cannot solve it. I would like to know if there is a way to find new boundary conditions for f'''[e]=... and f''[e]=... so that it would work. Thx

• Are you sure that this is a question for this site though? If the problem is in the formulation of your equations, then this is not a Mathematica or code problem. Perhaps you could expand on the origin of your equations; somebody might have worked with it before. – MarcoB Jun 26 '18 at 19:18
• I think it's a question for this site, because that maybe even now Mathematica doesn't like underconstrained differential equation, but it can propose constraints. Actually I remember that there are some techniques in some cases to do it with Mathematica, but I think it doesn't appply to my case. – J.A Jun 26 '18 at 19:35