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On a class of weakly regular singular two point boundary value problems. I. (English) Zbl 0853.34026
The author considers a class of singular two-point boundary value problems $- (p(x)y')' = p(x)$ $f(x,y)$, $0 < x \le b$, $y(0) = A$, $y(b) = B$. Applying a monotone iterative method directly to the singular problem, combined with an eigenfunction expansion, the author establishes an existence -- uniqueness result.

34B15Nonlinear boundary value problems for ODE
34B24Sturm-Liouville theory
34A45Theoretical approximation of solutions of ODE
34L10Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions (ODE)
Full Text: DOI
[1] Chawla, M.M.; Katti, C.P.: Finite difference methods and their convergence for a class of singular two point boundary value problems. Num. math 39, 341-350 (1982) · Zbl 0489.65055
[2] Chawla, M.M.; Katti, C.P.: A uniform mesh finite difference method for a class of singular two point boundary value problems. SIAM J. Numer. analysis 22, No. 3, 561-565 (1985) · Zbl 0578.65085
[3] Chawla, M.M.: A fourth-order finite difference method based on uniform mesh for a class of singular two point boundary value problems. J. comp. Appl. math. 17, 359-364 (1987) · Zbl 0614.65087
[4] Ciarlet, P.G.; Natterer, F.; Varga, R.S.: Numerical methods of higher-order accuracy for singular nonlinear boundary value problems. Num. math. 15, 87-99 (1970) · Zbl 0211.19103
[5] Iyengar, S.R.K.; Jain, P.: Spline finite difference methods for singular two point boundary value problems. Num. math. 50, 363-376 (1987) · Zbl 0642.65062
[6] Jain, M.K.: Fourth order difference method for the general second order singular boundary value problem with spherical symmetry. J. math. Phys. sci. 23, No. 3, 269-273 (1989) · Zbl 0681.65056
[7] Jamet, P.: On the convergence of finite-difference approximations to one dimensional singular boundary value problems. Num. math. 14, 355-378 (1970) · Zbl 0179.22103
[8] Sakai, M.; Usmani, R.A.: Non polynomial splines and weakly singular two point boundary value problems. Bit 28, 867-876 (1988) · Zbl 0665.65067
[9] Sakai, M.; Usmani, R.A.: An application of chawla’s identity to a different scheme for singular problems. Bit 29, 566-568 (1989) · Zbl 0705.65059
[10] Lees, M.: Discrete methods for nonlinear two point boundary value problems. Numerical solutions of partial differential equations, 59-72 (1966)
[11] Titchmarsh, E.C.: Eigenfunction expansions part I. (1962) · Zbl 0099.05201