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Erschienen in:
01.06.2012 | Original Research
Bessel functions and singular BVPs arising in physiology in the presence of upper and lower solutions in reverse order
Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2012
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Abstract
In this paper we consider a class of nonlinear singular boundary value problems of the type
where 1≤α≤β. When β=α and the nonlinear source function is f(x,y) or linear this problem arises in physiology (Adam and Maggelakis in Math. Biosci. 97:121–136, 1989; Anderson and Arthurs in Bull. Math. Biol. 47(1):145–153, 1985; Duggan and Goodman in Bull. Math. Biol. 48(2):229–236, 1989; Asaithambi and Garner in Appl. Math. Comput. 30:215–222, 1989) and in other branches of sciences and engineering (Keller in J. Ration. Mech. Anal. 5:715–724, 1956; Chamber in J. Chem. Phys. 20:1795–1797, 1952). In this work we establish existence of solutions when upper (u
0) and lower (v
0) solutions are ordered in one way (u
0≥v
0) or the other (u
0≤v
0). Though the proposed method in this paper is analytic, it is constructive in nature so that it can be implemented to compute approximate solutions.