ISSN:
1573-2878
Keywords:
Existence
;
periodic boundary-value problems
;
upper and lower solutions
;
convergence
;
quasilinearization
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, the results of Lakshmikantham et al. (Ref. 1) for first-order periodic boundary-value problems are extended, by using the extended method of quaislinearization and rapid convergence for initial-value problems of Mohapatra et al. (Ref. 2). Also, it is shown that monotone sequences converge cubically to the unique solution when the forcing function in the differential equation is 2–hyperconvex and converge quartically when the forcing function is 3–hyperconvex. Several other generalizations of the problem are also presented.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1021782529131
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