Unbounded solutions of BVP for second order ODE with p -Laplacian on the half line

Yuji Liu; Patricia J. Y. Wong

Applications of Mathematics (2013)

  • Volume: 58, Issue: 2, page 179-204
  • ISSN: 0862-7940

Abstract

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By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.

How to cite

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Liu, Yuji, and Wong, Patricia J. Y.. "Unbounded solutions of BVP for second order ODE with $p$-Laplacian on the half line." Applications of Mathematics 58.2 (2013): 179-204. <http://eudml.org/doc/252539>.

@article{Liu2013,
abstract = {By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.},
author = {Liu, Yuji, Wong, Patricia J. Y.},
journal = {Applications of Mathematics},
keywords = {second order differential equation on a half line; non-homogeneous boundary value problem; Leggett-Williams fixed point theorem; second order ODE; half-line; -Laplacian; three unbounded positive solutions; Leggett-Williams fixed point theorem},
language = {eng},
number = {2},
pages = {179-204},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Unbounded solutions of BVP for second order ODE with $p$-Laplacian on the half line},
url = {http://eudml.org/doc/252539},
volume = {58},
year = {2013},
}

TY - JOUR
AU - Liu, Yuji
AU - Wong, Patricia J. Y.
TI - Unbounded solutions of BVP for second order ODE with $p$-Laplacian on the half line
JO - Applications of Mathematics
PY - 2013
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 2
SP - 179
EP - 204
AB - By applying the Leggett-Williams fixed point theorem in a suitably constructed cone, we obtain the existence of at least three unbounded positive solutions for a boundary value problem on the half line. Our result improves and complements some of the work in the literature.
LA - eng
KW - second order differential equation on a half line; non-homogeneous boundary value problem; Leggett-Williams fixed point theorem; second order ODE; half-line; -Laplacian; three unbounded positive solutions; Leggett-Williams fixed point theorem
UR - http://eudml.org/doc/252539
ER -

References

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  1. Agarwal, R. P., O'Regan, D., Wong, P. J. Y., Positive Solutions of Differential, Difference and Integral Equations, Kluwer Academic Publishers Dordrecht (1999). (1999) Zbl1157.34301MR1680024
  2. Agarwal, R. P., O'Regan, D., Wong, P. J. Y., 10.1023/B:ACAP.0000013257.42126.ca, Acta Appl. Math. 80 (2004), 57-94. (2004) Zbl1053.45004MR2034575DOI10.1023/B:ACAP.0000013257.42126.ca
  3. Agarwal, R. P., O'Regan, D., Wong, P. J. Y., 10.1016/S0895-7177(04)90536-5, Math. Comput. Modelling 39 (2004), 1113-1150. (2004) Zbl1068.45001MR2069517DOI10.1016/S0895-7177(04)90536-5
  4. Agarwal, R. P., O'Regan, D., Wong, P. J. Y., Triple solutions of constant sign for a system of Fredholm integral equations, Cubo 6 (2004), 1-45. (2004) Zbl1082.45004MR2124824
  5. Djebali, S., Mebarki, K., 10.1016/j.camwa.2007.11.023, Comput. Math. Appl. 55 (2008), 2940-2952. (2008) Zbl1142.34316MR2401442DOI10.1016/j.camwa.2007.11.023
  6. Guo, Y., Yu, C., Wang, J., Existence of three positive solutions for m -point boundary value problems on infinite intervals, Nonlinear Anal., Theory Methods Appl. 71 (2009), 717-722. (2009) Zbl1172.34310MR2527493
  7. Kang, P., Wei, Z., 10.1016/j.amc.2007.06.004, Appl. Math. Comput. 196 (2008), 402-415. (2008) Zbl1136.34026MR2382579DOI10.1016/j.amc.2007.06.004
  8. Leggett, R. W., Williams, L. R., 10.1512/iumj.1979.28.28046, Indiana Univ. Math. J. 28 (1979), 673-688. (1979) Zbl0421.47033MR0542951DOI10.1512/iumj.1979.28.28046
  9. Lian, H., Ge, W., 10.1016/j.aml.2005.10.018, Appl. Math. Lett. 19 (2006), 1000-1006. (2006) Zbl1123.34307MR2246166DOI10.1016/j.aml.2005.10.018
  10. Lian, H., Ge, W., 10.1016/j.jmaa.2005.09.001, J. Math. Anal. Appl. 321 (2006), 781-792. (2006) Zbl1104.34020MR2241155DOI10.1016/j.jmaa.2005.09.001
  11. Lian, H., Pang, H., Ge, W., 10.1016/j.na.2006.09.016, Nonlinear Anal., Theory Methods Appl. 67 (2007), 2199-2207. (2007) Zbl1128.34011MR2331870DOI10.1016/j.na.2006.09.016
  12. Lian, H., Pang, H., Ge, W., 10.1016/j.jmaa.2007.04.038, J. Math. Anal. Appl. 337 (2008), 1171-1181. (2008) Zbl1136.34034MR2386366DOI10.1016/j.jmaa.2007.04.038
  13. Lian, H., Pang, H., Ge, W., Unbounded upper and lower solutions method for Sturm-Liouville boundary value problem on infinite intervals, Nonlinear Anal., Theory Methods Appl. 70 (2009), 2627-2633. (2009) MR2499729
  14. Liang, S., Zhang, J., 10.1016/j.amc.2007.12.016, Appl. Math. Comput. 201 (2008), 210-220. (2008) Zbl1157.34016MR2432596DOI10.1016/j.amc.2007.12.016
  15. Liang, S., Zhang, J., 10.1016/j.cam.2007.10.062, J. Comput. Appl. Math. 222 (2008), 229-243. (2008) Zbl1183.34031MR2474626DOI10.1016/j.cam.2007.10.062
  16. Liang, S., Zhang, J., The existence of countably many positive solutions for some nonlinear three-point boundary problems on the half-line, Nonlinear Anal., Theory Methods Appl. 70 (2009), 3127-3139. (2009) Zbl1166.34304MR2503058
  17. Liu, Y., The existence of three positive solutions to integral type BVPs for second order ODEs with one-dimensional p -Laplacian, Bull. Malays. Math. Sci. Soc. (2) 35 359-372 (2012). (2012) Zbl1243.34036MR2893462
  18. Liu, Y., Boundary value problem for second order differential equations on unbounded domains, Acta Anal. Funct. Appl. 4 (2002), 211-216 Chinese. (2002) Zbl1038.34030MR1956716
  19. Liu, Y., 10.1016/S0096-3003(02)00431-9, Appl. Math. Comput. 144 (2003), 543-556. (2003) Zbl1036.34027MR1994092DOI10.1016/S0096-3003(02)00431-9
  20. O'Regan, D., Yan, B., Agarwal, R. P., 10.1016/j.cam.2006.02.055, J. Comput. Appl. Math. 205 (2007), 751-763. (2007) Zbl1124.34008MR2329651DOI10.1016/j.cam.2006.02.055
  21. Palamides, P. K., Galanis, G. N., Positive, unbounded and monotone solutions of the singular second Painlevé equation on the half-line, Nonlinear Anal., Theory Methods Appl. 57 (2004), 401-419. (2004) Zbl1053.34028MR2064098
  22. Tian, Y., Ge, W., 10.1016/j.jmaa.2006.02.075, J. Math. Anal. Appl. 325 (2007), 1339-1349. (2007) Zbl1110.34018MR2270088DOI10.1016/j.jmaa.2006.02.075
  23. Wei, Y., Wong, P. J. Y., Ge, W., 10.1016/j.cam.2009.10.005, J. Comput. Appl. Math. 233 (2010), 2189-2199. (2010) Zbl1187.34086MR2577758DOI10.1016/j.cam.2009.10.005
  24. Yan, B., Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line, Nonlinear Anal., Theory Methods Appl. 51 (2002), 1031-1044. (2002) Zbl1021.34021MR1926083
  25. Yan, B., Liu, Y., 10.1016/S0096-3003(02)00801-9, Appl. Math. Comput. 147 (2004), 629-644. (2004) Zbl1045.34009MR2011077DOI10.1016/S0096-3003(02)00801-9
  26. Yan, B., O'Regan, D., Agarwal, R. P., 10.1016/j.cam.2005.11.010, J. Comput. Appl. Math. 197 (2006), 365-386. (2006) Zbl1116.34016MR2260412DOI10.1016/j.cam.2005.11.010
  27. Yan, B., O'Regan, D., Agarwal, R. P., Positive solutions for second order singular boundary value problems with derivative dependence on infinite intervals, Acta Appl. Math. 103 (2008), 19-57. (2008) Zbl1158.34011MR2415171
  28. Yan, B., Timoney, R. M., Positive solutions for nonlinear singular boundary value problems on the half line, Int. J. Math. Anal., Ruse 1 (2007), 1189-1208. (2007) Zbl1149.34011MR2382022
  29. Zhang, X., Liu, L., Wu, Y., 10.1016/j.amc.2006.07.056, Appl. Math. Comput. 185 (2007), 628-635. (2007) Zbl1117.34033MR2297833DOI10.1016/j.amc.2006.07.056
  30. Zima, M., 10.1006/jmaa.2000.7399, J. Math. Anal. Appl. 259 (2001), 127-136. (2001) Zbl1003.34024MR1836449DOI10.1006/jmaa.2000.7399

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