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Solvability of singular nonlinear two-point boundary value problems. (English) Zbl 0876.34017
This paper discusses singular nonlinear boundary value problems. In particular the differential equation $\frac{1}{h(t)} (h(t)y'(t))'= g(t)F(t,y(t))=0, \qquad 0<t<1$ with Dirichlet or mixed boundary data is examined. Under suitable assumptions (see Theorem 1 and Theorem 2) the authors establish the existence of a solution. Although the results of the paper are new, the technique involved however is standard. The paper is well written and some nice examples are given at the end to illustrate the theory involved.

##### MSC:
 34B15 Nonlinear boundary value problems for ordinary differential equations
##### Keywords:
singular nonlinear boundary value problems
Full Text:
##### References:
  Bobisud, L.E., Existence of solutions for nonlinear singular boundary value problems, Applic. analysis, 35, 43-57, (1990) · Zbl 0666.34017  Bobisud, L.E.; O’regan, D.; Royalty, W.D., Singular boundary value problems, Applic. analysis, 23, 233-243, (1986) · Zbl 0584.34012  Chan, C.Y.; Hon, C., A constructive solution for a generalized Thomas-Fermi theory of ionized atoms, Q. appl. math., 45, 591-599, (1987) · Zbl 0639.34021  Dunninger, D.R.; Kurtz, J.C., A priori bounds and existence of positive solutions for singular nonlinear boundary value problems, SIAM J. math. analysis, 17, 595-609, (1986) · Zbl 0595.34016  Dunninger, D.R.; Kurtz, J.C., Existence of solutions for some nonlinear singular boundary value problems, J. math. analysis applic., 115, 369-405, (1986) · Zbl 0616.34012  Gatica, J.A.; Oliker, V.; Waltman, P., Singular nonlinear boundary value problems for second order ordinary differential equations, J. diff. eqns, 79, 62-78, (1989) · Zbl 0685.34017  Mawhin, T.; Omana, W., Two point boundary value problems for nonlinear perturbations of some singular linear differential equations at resonance, Commentat. math. univ. carolinae, 30, 3, 537-550, (1989) · Zbl 0686.34014  Bobisud, L.E.; O’regan, D.; Royalty, W.D., Solvability of some nonlinear boundary value problems, Nonlinear analysis, 12, 855-869, (1988) · Zbl 0653.34015  Callegari, A.; Nachmann, A., A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. appl. math., 38, 275-281, (1980) · Zbl 0453.76002  Luning, C.D.; Perry, W.L., Positive solutions of negative exponent generalized emder-Fowler boundary value problems, SIAM J. math. analysis, 12, 874-879, (1981) · Zbl 0478.34021  O’regan, D., Positive solutions to singular and nonsingular second order boundary value problems, J. math. analysis applic., 142, 40-52, (1989) · Zbl 0689.34015  O’regan, D., Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. diff. eqns, 84, 228-251, (1990) · Zbl 0706.34030  O’regan, D., Some existence principles and some general results for singular nonlinear two point boundary value problems, J. math. analysis applic., 166, 24-40, (1992) · Zbl 0756.34030  Taliaferro, S., A nonlinear singular boundary value problem, Nonlinear analysis, 3, 897-904, (1979) · Zbl 0421.34021  Wang, Junyu, Singular two-point boundary value problems, Northeastern math. J., 3, 218-291, (1987) · Zbl 0669.34023
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