A note on the existence of positive solutions of one-dimensional p -Laplacian boundary value problems

Yuji Liu

Applications of Mathematics (2010)

  • Volume: 55, Issue: 3, page 241-264
  • ISSN: 0862-7940

Abstract

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This paper is concerned with the existence of positive solutions of a multi-point boundary value problem for higher-order differential equation with one-dimensional p -Laplacian. Examples are presented to illustrate the main results. The result in this paper generalizes those in existing papers.

How to cite

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Liu, Yuji. "A note on the existence of positive solutions of one-dimensional $p$-Laplacian boundary value problems." Applications of Mathematics 55.3 (2010): 241-264. <http://eudml.org/doc/37846>.

@article{Liu2010,
abstract = {This paper is concerned with the existence of positive solutions of a multi-point boundary value problem for higher-order differential equation with one-dimensional $p$-Laplacian. Examples are presented to illustrate the main results. The result in this paper generalizes those in existing papers.},
author = {Liu, Yuji},
journal = {Applications of Mathematics},
keywords = {one-dimension $p$-Laplacian differential equation; nonlocal boundary value problem; positive solution; fixed-point theorem; one-dimension -Laplacian differential equation; nonlocal boundary value problem; positive solution; fixed-point theorem},
language = {eng},
number = {3},
pages = {241-264},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A note on the existence of positive solutions of one-dimensional $p$-Laplacian boundary value problems},
url = {http://eudml.org/doc/37846},
volume = {55},
year = {2010},
}

TY - JOUR
AU - Liu, Yuji
TI - A note on the existence of positive solutions of one-dimensional $p$-Laplacian boundary value problems
JO - Applications of Mathematics
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 55
IS - 3
SP - 241
EP - 264
AB - This paper is concerned with the existence of positive solutions of a multi-point boundary value problem for higher-order differential equation with one-dimensional $p$-Laplacian. Examples are presented to illustrate the main results. The result in this paper generalizes those in existing papers.
LA - eng
KW - one-dimension $p$-Laplacian differential equation; nonlocal boundary value problem; positive solution; fixed-point theorem; one-dimension -Laplacian differential equation; nonlocal boundary value problem; positive solution; fixed-point theorem
UR - http://eudml.org/doc/37846
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 Dordrecht (1999). (1999) Zbl1157.34301MR1680024
  2. Bai, C., Fang, J., 10.1016/S0096-3003(02)00227-8, Appl. Math. Comput. 140 (2003), 297-305. (2003) Zbl1030.34026MR1953901DOI10.1016/S0096-3003(02)00227-8
  3. Bai, C., Fang, J., 10.1016/S0022-247X(02)00509-7, J. Math. Anal. Appl. 281 (2003), 76-85. (2003) MR1980075DOI10.1016/S0022-247X(02)00509-7
  4. delPino, M. A., Elgueta, M., Manásevich, R. F., 10.1016/0022-0396(89)90093-4, J. Differ. Equ. 80 (1989), 1-13. (1989) MR1003248DOI10.1016/0022-0396(89)90093-4
  5. delPino, M. A., Manásevich, R. F., Multiple solutions for the p -Laplacian under global nonresonance, Proc. Am. Math. Soc. 112 (1991), 131-138. (1991) MR1045589
  6. Gaines, R. E., Mawhin, J. L., 10.1007/BFb0089537, Springer Berlin (1977). (1977) MR0637067DOI10.1007/BFb0089537
  7. Guo, Y., Ge, W., 10.1016/S0022-247X(03)00476-1, J. Math. Anal. Appl. 286 (2003), 491-508. (2003) MR2008845DOI10.1016/S0022-247X(03)00476-1
  8. Ji, D., Feng, M., Ge, W., 10.1016/j.amc.2007.06.028, Appl. Math. Comput. 196 (2008), 511-520. (2008) Zbl1138.34014MR2388707DOI10.1016/j.amc.2007.06.028
  9. Karakostas, G. L., Triple positive solutions for the Φ -Laplacian when Φ is a sup-multiplicative-like function, Electron. Diff. Equ. 69 (2004), 1-13. (2004) Zbl1057.34010MR2057656
  10. Karakostas, G. L., Positive solutions for the Φ -Laplacian when Φ is a sup-multiplicative-like function, Electron. Diff. Equ. 68 (2004), 1-12. (2004) Zbl1057.34010MR2057655
  11. Kosmatov, N., 10.1016/j.jmaa.2004.11.008, J. Math. Anal. Appl. 309 (2005), 25-36. (2005) Zbl1085.34011MR2154024DOI10.1016/j.jmaa.2004.11.008
  12. Lan, K. D., 10.1112/S002461070100206X, J. Lond. Math. Soc., Ser. II 63 (2001), 690-704. (2001) Zbl1032.34019MR1825983DOI10.1112/S002461070100206X
  13. Lian, W.-C., Wong, F., 10.1016/S0893-9659(00)00051-3, Appl. Math. Lett. 13 (2000), 35-43. (2000) Zbl0964.34018MR1772689DOI10.1016/S0893-9659(00)00051-3
  14. Liang, R., Peng, J., Shen, J., 10.1016/j.amc.2007.07.025, Appl. Math. Comput. 196 (2008), 931-940. (2008) Zbl1140.34313MR2388746DOI10.1016/j.amc.2007.07.025
  15. Liu, B., 10.1016/S0096-3003(03)00770-7, Appl. Math. Comput. 155 (2004), 179-203. (2004) Zbl1068.34011MR2078102DOI10.1016/S0096-3003(03)00770-7
  16. Liu, Y., Ge, W., 10.1016/S0022-247X(02)00557-7, J. Math. Anal. Appl. 277 (2003), 293-302. (2003) Zbl1026.34028MR1954477DOI10.1016/S0022-247X(02)00557-7
  17. Lü, H., O'Regan, D., Zhong, C., 10.1016/S0096-3003(01)00240-5, Appl. Math. Comput. 133 (2002), 407-422. (2002) MR1924626DOI10.1016/S0096-3003(01)00240-5
  18. Ma, R., 10.1017/S0013091502000391, Proc. Edinb. Math. Soc., II. Ser. 46 (2003), 279-292. (2003) Zbl1069.34036MR1998561DOI10.1017/S0013091502000391
  19. Ma, R., 10.1016/S0362-546X(99)00152-2, Nonlinear Anal., Theory Methods Appl. 42 (2000), 1003-1010. (2000) Zbl0973.34014MR1780450DOI10.1016/S0362-546X(99)00152-2
  20. Ma, R., 10.1007/s10587-006-0092-7, Czech. Math. J. 56 (2006), 1243-1263. (2006) Zbl1164.34329MR2280807DOI10.1007/s10587-006-0092-7
  21. Ma, R., Castaneda, N., 10.1006/jmaa.2000.7320, J. Math. Anal. Appl. 256 (2001), 556-567. (2001) Zbl0988.34009MR1821757DOI10.1006/jmaa.2000.7320
  22. Ma, R., Thompson, B., 10.1016/j.jmaa.2003.12.046, J. Math. Anal. Appl. 297 (2004), 24-37. (2004) Zbl1057.34011MR2079645DOI10.1016/j.jmaa.2003.12.046
  23. Wang, Y., Zhao, W., Ge, W., 10.1016/j.jmaa.2006.03.028, J. Math. Anal. Appl. 326 (2007), 641-654. (2007) Zbl1119.34050MR2277809DOI10.1016/j.jmaa.2006.03.028
  24. Webb, J. R. L., 10.1016/S0362-546X(01)00547-8, Nonlinear Anal., Theory Methods Appl. 47 (2001), 4319-4332. (2001) Zbl1042.34527MR1975828DOI10.1016/S0362-546X(01)00547-8
  25. Zhang, G., Sun, J., 10.1016/j.jmaa.2003.11.034, J. Math. Anal. Appl. 291 (2004), 406-418. (2004) Zbl1069.34037MR2038179DOI10.1016/j.jmaa.2003.11.034
  26. Zhang, Z., Wang, J., 10.1016/j.jmaa.2004.03.057, J. Math. Anal. Appl. 295 (2004), 502-512. (2004) Zbl1056.34018MR2072028DOI10.1016/j.jmaa.2004.03.057

Citations in EuDML Documents

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  1. Luís Almeida, Lucio Damascelli, Yuxin Ge, A few symmetry results for nonlinear elliptic PDE on noncompact manifolds
  2. Mohamed Saad Bouh Elemine Vall, Ahmed Ahmed, Abdelfattah Touzani, Abdelmoujib Benkirane, Entropy solutions to parabolic equations in Musielak framework involving non coercivity term in divergence form
  3. Stanislav I Pohozaev, Alberto Tesei, Nonexistence of local solutions to semilinear partial differential inequalities
  4. Patrizia Pucci, Raffaella Servadei, Existence, non-existence and regularity of radial ground states for p-laplacian equations with singular weights

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