This is the first time I ask a question. I have seen many solutions to this error and tried but they are not working.

Here is the code.

Needs["DifferentialEquationsNDSolveProblems"];

Needs["DifferentialEquationsNDSolveUtilities"];

Needs["FunctionApproximations`"];

Clear["Global`*"];

e = 1.60217662*10^-19;

c = 299792458;

m = 9.10938356*10^-31;

[Epsilon]0 = 8.854187817*10^-12;

A = 10^17;

h = 6.6260700410^-34; hbar = 1.054571810^-34; k = 1/[Epsilon]0 (2 e/h^3) (4 Pi/3);

x0 = (3/(4 Pi) A1.6043957210^-24/(4*10^14))^(1/3)/100;

xf = 10^0;

s = NDSolve[{1/x D[x y[x], {x, 2}] == k ((e y[x]/c)^2 + 2 m*e y[x])^1.5, y[x0] == 10^6, y[xf] == 10^-5}, y[x], {x, x0, xf}]

xf should be infinity but NDSolve doesn't allow infinity so I put a relatively large number.

y[xf] is also needed to be zero at infinity. I put a relatively small number since I expected that y[x] is close to zero when x is approaching infinity.

Here is the error:

At x == 0.112455460174063`, step size is effectively zero; singularity or stiff system suspected. >>