Positive Solutions for a Boundary Value Problem with a Derivative Argument

DOI: 10.4236/jamp.2013.14014   PDF        6,612 Downloads   8,145 Views  


In this paper, several existence results of multiple positive solutions are obtained for a boundary value problem with p-Laplacian, by applying a fixed point theorem in cones. The interesting point is that the nonlinear term f is involved with the first-order derivative explicitly.

Share and Cite:

Sun, B. (2013) Positive Solutions for a Boundary Value Problem with a Derivative Argument. Journal of Applied Mathematics and Physics, 1, 73-77. doi: 10.4236/jamp.2013.14014.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] D. Guo, “Multiple Positive Solutions on Nonlinear Integral Equations and Applications,” Applicable Analysis, Vol. 23, No. 1-2, 1986, pp. 77-84. http://dx.doi.org/10.1080/00036818608839632
[2] X. He, W. Ge and M. Peng, “Multiple Positive solutions for One-Dimensional p-Laplacian Boundary Value Problems,” Applied Mathematics Letters, Vol. 15, No. 8, 2002, pp. 937-943. http://dx.doi.org/10.1016/S0893-9659(02)00067-8
[3] R. Y. Ma and D. M. Cao, “Positive Solutions to an m-Point Boundary Value Problem,” Applied Mathematics—A Journal of Chinese Universities, Vol. 17, No. 1, 2002, pp. 24-30. http://dx.doi.org/10.1007/s11766-002-0021-y
[4] B. Liu and J. S. Yu, “Solvability of Multi-Point Boundary Value Problems at Resonance(I),” India J. Pure Appl. Math., Vol. 33, 2002, pp. 475-494.
[5] J. Henderson and H. Wang, “Positive Solutions for Nonlinear Eigenvalue Problems,” Journal of Mathematical Analysis and Applications, Vol. 208, No. 1, 1997, pp. 252-259. http://dx.doi.org/10.1006/jmaa.1997.5334
[6] R. Ma and N. Castaneda, “Existence of Solutions of Nonlinear m-Point Boundary Value Problems,” Journal of Mathematical Analysis and Applications, Vol. 256, No. 2, 2001, pp. 556-567. http://dx.doi.org/10.1006/jmaa.2000.7320
[7] D. Guo and V. Lakshmikantham, “Nonlinear Problems in Abstract Cones,” Academic Press, New York, 1988.
[8] D. Ma, Z. Du and W. Ge, “Existence and Iteration of Monotone Positive Solutions for Multipoint Boundary Value Problems with p-Laplacian Operator,” Computers & Mathematics with Applications, Vol. 50, No. 5-6, 2005, pp. 729-739. http://dx.doi.org/10.1016/j.camwa.2005.04.016
[9] Y. Wang and C. Hou, “Existence of Triple Positive Solu- tions for Multi-Point Boundary Value Problems with a One-Dimensional p-Laplacian,” Computers & Mathematics with Applications, Vol. 54, No. 6, 2007, pp. 793- 807. http://dx.doi.org/10.1016/j.camwa.2006.10.038

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.