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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["DifferentialEquations`NDSolveProblems`"];
 
Needs["DifferentialEquations`NDSolveUtilities`"];
 
Needs["FunctionApproximations`"];

Clear["Global`*"];

e = 1.60217662*10^-19;
 
c = 299792458;
 
m = 9.10938356*10^-31;
 
ϵ0 = 8.854187817*10^-12;
 
A = 10^17;
 
h = 6.62607004*10^-34; hbar = 1.0545718*10^-34;
 k = 
 1/ϵ0 (2 e/h^3) (4 Pi/3);
 
 x0 = (3/(4 *Pi)*
     A*1.60439572*10^-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. >>

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["DifferentialEquations`NDSolveProblems`"];
Needs["DifferentialEquations`NDSolveUtilities`"];
Needs["FunctionApproximations`"];

Clear["Global`*"];

e = 1.60217662*10^-19;
c = 299792458;
m = 9.10938356*10^-31;
ϵ0 = 8.854187817*10^-12;
A = 10^17;
h = 6.62607004*10^-34; hbar = 1.0545718*10^-34;
k = 1/ϵ0 (2 e/h^3) (4 Pi/3);
x0 = (3/(4 *Pi)*A*1.60439572*10^-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. >>