Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
singular conjugate BVP; positive solutions; zeros of derivatives; estimates from below
singular conjugate BVP; positive solutions; zeros of derivatives; estimates from below
Summary:
Positive solutions of the singular $(p,n-p)$ conjugate BVP are studied. The set of all zeros of their derivatives up to order $n-1$ is described. By means of this, estimates from below of the solutions and the absolute values of their derivatives up to order $n-1$ on the considered interval are reached. Such estimates are necessary for the application of the general existence principle to the BVP under consideration.
References:
[1] Agarwal R. P., O’Regan D.: Positive solutions for (p,n-p) conjugate boundary value problems. J. Differential Equations 150 (1998), 462–473. MR 1658664 | Zbl 0920.34027
[2] Agarwal R. P., O’Regan D.: Multiplicity results for singular conjugate, focal, and $(n,p)$ problems. J. Differential Equations 170 (2001), 142–156. MR 1813103 | Zbl 0978.34018
[3] Agarwal R. P., O’Regan D., Rachůnková I., Staněk S.: Two-point higher order BVPs with singularities in phase variables. Computers & Mathematics with Applications 46 (2003), 1799–1826. MR 2018767 | Zbl 1057.34005
[4] Eloe P. W., Henderson J.: Singular nonlinear $(n-1,1)$ conjugate boundary value problems. Georgian Math. J. 4 (1997), 401–412. MR 1469324 | Zbl 0882.34029
[5] Eloe P. W., Henderson J.: Singular nonlinear $(k,n-k)$ conjugate boundary value problems. J. Differential Equations 133 (1997), 136–151. MR 1426760 | Zbl 0870.34031
[6] Rachůnková I., Staněk S.: General existence principle for singular BVPs and its applications. Georgian Math. J. 11 (2004), 549–565. MR 2081745
Search
Partner of
