Computational methods for generalized Thomas-Fermi models of neutral atoms

Solvability of Some Singular Boundary Value Problems on the Semi-Infinite Interval

“…Section 3 will now use the results of Section 2 to establish existence of solutions to (1.1). Again here the results are new and extend and complement the existing theory found in [4,11,12]. Finally it is easy to see that the linear problem…”

“…for each n G TV 4 ". Various existence results for problems of the form (1.2) will be obtained by exploiting the properties of the zero set off.…”

“…Boundary value problems on the semi-infinite interval have been examined extensively over the last ten years or so with most of the results obtained for the nonsingular problem (p = q = 1); see [1,2,6,7] and their references. However recently [4,11,12] some results for nonsingular problems have been obtained. These papers were motivated by the Thomas-Fermi equation y" = r*yK 0<t<oo subject to the boundary condition corresponding to the isolated neutral atom 7(0) =1, limX0 = 0.…”

Continuous and discrete boundary value problems on the infinite interval: existence theory

“…Section 2 discusses the continuous boundary value problems (here a s= 0 is fixed) Several special cases of (1.1) have been discussed in the literature (see [3][4][5][6][7][8][10][11] and the references therein). Here we present a general theory which includes the results in [3][4][5][6][7][8][9][10][11][12]. We illustrate in Section 2 the generality of our results by discussing a problem which arises in the flow and heat transfer over a stretching sheet [12], namely, y -\+y y(a) = b, lim y(t) = 0, (1.3) [MATHEMATIKA, 48 (2001), [273][274][275][276][277][278][279][280][281][282][283][284][285][286][287][288][289][290][291][292] where a > 0, b > 0, B > 0 are constants with A < 0 if R > 0, whereas Re " -A > 0 if/?=£().…”