Imposing boundary condition at infinity

*To*: mathgroup at smc.vnet.net*Subject*: [mg63228] Imposing boundary condition at infinity*From*: dkjk at bigpond.net.au*Date*: Mon, 19 Dec 2005 07:02:04 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hi all, I need to solve a differential equation whose solution has the contraint that it tends to zero in the infinite limit. Mathematica will not, however, allow \[Phi][Infinity]==0 as one of the contraints. Does mathematica have another notation for dealing with this constraint? Thanks. James \!\(DSolve[{\(1\/r\^2\) D[r\^2*D[Ï?[r], r], r] == \(1\/Ïµ\) \((Ï?[r] \((\(2*ec^2*n0\)\/\(k*T\))\) + \(27* q\)\/\(2*Pi* a\^3*\@\(2*Pi\)\)* Exp[\(-\(\(9 r^2\)\/\(2 a^2\)\)\)])\), Ï?[0] == \(\(3\ \@2\ \ q\ Î»\)\/Ï?\^\(3/2\) - \(\[ExponentialE]\^\(a\^2\/\(18\ Î»\^2\)\)\ q\ \ \@\(a\^2\/Î»\^2\)\ Î»\)\/Ï? + \(a\ \[ExponentialE]\^\(a\^2\/\(18\ Î»\^2\)\)\ q\ Erf[a\/\(3\ \@2\ Î»\)]\)\/ Ï?\)\/\(4\ a\ Ïµ\ Î»\), Ï?[Infinity] == 0}, Ï?, r]\)