Positive and maximal positive solutions of singular mixed boundary value problem

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1. [1] Agarwal R.P., O’Regan D., Singular differential and integral equations with applications, Kluwer, Dordrecht, 2003 
2. [2] Agarwal R.P., O’Regan D., Singular problems motivated from classical upper and lower solutions, Acta Math. Hungar., 2003, 100, 245–256 http://dx.doi.org/10.1023/A:1025045626822[Crossref] 
3. [3] Agarwal R.P., O’Regan D., Staněek S., Existence of positive solutions for boundary-value problems with singularities in phase variables, Proc. Edinburgh Math. Soc., 2004, 47, 1–13 http://dx.doi.org/10.1017/S0013091503000105[Crossref] 
4. [4] Agarwal R.P., Staněek S., Nonnegative solutions of singular boundary value problems with sign changing nonlinearities, Comput. Math. Appl., 2003, 46, 1827–1837 http://dx.doi.org/10.1016/S0898-1221(03)90239-2[Crossref] Zbl1156.34310
5. [5] Bartle R.G., A modern theory of integrations, AMS Providence, Rhode Island, 2001 Zbl0968.26001
6. [6] Berestycki H., Lions P.L., Peletier L.A., An ODE approach to the existence of positive solutions for semilinear problems in ℝN, Indiana Univ. Math. J., 1981, 30, 141–157 http://dx.doi.org/10.1512/iumj.1981.30.30012[Crossref] 
7. [7] Bertsch M., Passo R.D., Ughi M., Discontinuous viscosity solutions of a degenerate parabolic equation, Trans. Amer. Math. Soc., 1990, 320, 779–798 http://dx.doi.org/10.2307/2001703[Crossref] Zbl0714.35039
8. [8] Bertsch M., Ughi M., Positive properties of viscosity solutions of a degenerate parabolic equation, Nonlinear Anal., 1990, 14, 571–592 http://dx.doi.org/10.1016/0362-546X(90)90063-M[Crossref] 
9. [9] Cabada A., Cid J.A., Extremal solutions of ϕ-Laplacian-diffusion scalar problems with nonlinear functional boundary conditions in a unified way, Nonlinear. Anal., 2005, 63, 2515–2524 http://dx.doi.org/10.1016/j.na.2004.09.031[Crossref] 
10. [10] Cabada A., Nieto J.J., Extremal solutions of second order nonlinear periodic boundary value problems, Appl. Math. Comput., 1990, 40, 135–145 http://dx.doi.org/10.1016/0096-3003(90)90128-P[Crossref] 
11. [11] Cabada A., Pouso R.P., Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions, Nonlinear Anal., 2000, 42, 1377–1396 http://dx.doi.org/10.1016/S0362-546X(99)00158-3[Crossref] Zbl0964.34016
12. [12] Carl S., Heikkilä S., Nonlinear differential equations in ordered spaces, Chapman & Hall/CRC, Monographs and Surveys in Pure and Applied Mathematics III, 2000 
13. [13] Castro A., Sudhasree G., Uniqueness of stable and unstable positive solutions for semipositone problems, Nonlinear Anal., 1994, 22, 425–429 http://dx.doi.org/10.1016/0362-546X(94)90166-X[Crossref] Zbl0804.35038
14. [14] Cherpion M., De Coster C., Habets P., Monotone iterative method for boundary value problem, Differential integral equations, 1999, 12, 309–338 Zbl1015.34009
15. [15] Cid J.A., On extremal fixed point in Schauder’s theorem with application to differential equations, Bull. Belg. Math. Soc. Simon Stevin, 2004, 11, 15–20 Zbl1076.47044
16. [16] Gidas B., Ni W.M., Nirenberg L., Symmetry of positive solutions of nonlinear elliptic equations in ℝN, Adv. Math., Suppl. Stud. 7A, 1981, 369–402 
17. [17] Kelevedjiev P., Nonnegative solutions to some singular second-order boundary value problems, Nonlinear Anal., 1999, 36, 481–494 http://dx.doi.org/10.1016/S0362-546X(98)00025-X[Crossref] Zbl0929.34022
18. [18] Kiguradze I., Some optimal conditions for solvability of two-point singular boundary value problems, Funct. Differ. Equ., 2003, 10, 259–281 Zbl1062.34017
19. [19] Kiguradze I.T., Shekhter B.L., Singular boundary value problems for second order ordinary differential equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Nov. Dostizh., 1987, 30, 105–201 (in Russian), English translation: Journal of Soviet Mathematics, 1988, 43, 2340–2417 Zbl0782.34026
20. [20] Lang S., Real and functional analysis, Springer, New York, 1993 Zbl0831.46001
21. [21] O’Regan D., Existence of positive solutions to some singular and nonsingular second order boundary value problems, J. Differential Equations, 1990, 84, 228–251 http://dx.doi.org/10.1016/0022-0396(90)90077-3[Crossref] 
22. [22] Rachůnková I., Singular mixed boundary value problem, J. Math. Anal. Appl., 2006, 320, 611–618 http://dx.doi.org/10.1016/j.jmaa.2005.07.037[Crossref] 
23. [23] Rachůnková I., Staněk S., Connections between types of singularities in differential equations and smoothness of solutions for Dirichlet BVPs, Dyn. Contin. Discrete Impuls. Syst. Ser. A. Math. Anal., 2003, 10, 209–222 Zbl1043.34022
24. [24] Rachůnková I., Staněk S., Tvrdý M., Singularities and laplacians in boundary value problems for nonlinear differential equations, In: Cañada A., Drábek P., Fonda A. (Eds.), Handbook of differential equations, Ordinary differential equations, Vol. 3, 607–723, Elsevier, 2006 
25. [25] Thompson H.B., Second order ordinary differential equations with fully nonlinear two point boundary conditions, Pacific J. Math., 1996, 172, 255–277 Zbl0855.34024
26. [26] Thompson H.B., Second order ordinary differential equations with fully nonlinear two point boundary conditions II, Pacific J. Math., 1996, 172, 259–297 Zbl0862.34015
27. [27] Wang J., Gao W., A note on singular nonlinear two-point boundary value problems, Nonlinear Anal., 2000, 39, 281–287 http://dx.doi.org/10.1016/S0362-546X(98)00165-5[Crossref] Zbl0942.34018
28. [28] Zheng L., Su X., Zhang X., Similarity solutions for boundary layer flow on a moving surface in an otherwise quiescent fluid medium, Int. J. Pure Appl. Math., 2005, 19, 541–552 Zbl1080.34008