Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System

Wang Feng; Junmin Zhang

doi:doi:10.11648/j.pamj.20130206.12

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Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System

Wang Feng, Junmin Zhang

Published in Pure and Applied Mathematics Journal (Volume 2, Issue 6)

Received: 11 November 2013 Accepted: Published: 10 December 2013

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Abstract

By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.

Published in	Pure and Applied Mathematics Journal (Volume 2, Issue 6)
DOI	10.11648/j.pamj.20130206.12
Page(s)	179-183
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Superlinear Singular Semipositone Differential System, Positive Solution, Fixed Point Theorem, Cone

References

[1]	Guo Dajun, Lakshmikantham V, Nonlinear problems in abstract cones[M],San Diego: Academic Press,1998, 24-56.
[2]	Anuradha V, Hai D, Shivaji R, Existence results for superlin- ear semipositone BVP’s[J], Pro Amer Math Soc, 1996, 124(3): 747-763.
[3]	Agarwal R P, O’Regan D, A note on existence of nonnegative solutions to singular semipositone problems[J], Nonlinear Anal, 1999, 36(5): 615-622.
[4]	Xu Xian, Positive solutions for singular semipositone boundary value problems[J], J Math Anal Appl, 2002,273(2): 480-491.
[5]	Zhang Xinguang, Liu Lishan, Positive solutions of superlinear semipositone singular Dirichlet boundary value problems[J], J Math Anal Appl, 2006, 316(2): 525-537.
[6]	Zhang Xinguang, Zhao Zenqin, Positive solution of fourth order singular semipositone boundary value problem[J], J Systems Sci Math Sci, 2006, 26(5): 553-560.
[7]	Fink A M, Gatica J A, Positive solutions of second order systems of boundary value problems[J], J Math Anal Appl, 1993, 180(1): 93-108.
[8]	Agarwal R P, O’Regan D, A coupled system of boundary value problems[J], Appl Anal, 1998, 69: 381-385.
[9]	Xu Xian, Positive solutions for singular semipositone three- point systems[J], Nonlinear Anal, 2007, 66: 791-805.
[10]	Liu Lishan, Zhang Xinguang, Wu Yonghong, On existence of positive solutions of a two-point boundary problem for a nonlinear singular semipositone system[J], Appl Math Comput, 2007, 192: 223-232.

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APA Style

Wang Feng, Junmin Zhang. (2013). Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System. Pure and Applied Mathematics Journal, 2(6), 179-183. https://doi.org/10.11648/j.pamj.20130206.12

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ACS Style

Wang Feng; Junmin Zhang. Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System. Pure Appl. Math. J. 2013, 2(6), 179-183. doi: 10.11648/j.pamj.20130206.12

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AMA Style

Wang Feng, Junmin Zhang. Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System. Pure Appl Math J. 2013;2(6):179-183. doi: 10.11648/j.pamj.20130206.12

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@article{10.11648/j.pamj.20130206.12,
  author = {Wang Feng and Junmin Zhang},
  title = {Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {6},
  pages = {179-183},
  doi = {10.11648/j.pamj.20130206.12},
  url = {https://doi.org/10.11648/j.pamj.20130206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.12},
  abstract = {By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.},
 year = {2013}
}

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TY  - JOUR
T1  - Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System
AU  - Wang Feng
AU  - Junmin Zhang
Y1  - 2013/12/10
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130206.12
DO  - 10.11648/j.pamj.20130206.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 179
EP  - 183
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130206.12
AB  - By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.
VL  - 2
IS  - 6
ER  -

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Author Information

Wang Feng

Jiangsu Union Technical Institute, Yancheng College of Mechatronic Technology, Yancheng, Jiangsu 224005, China
Junmin Zhang

Department of Mathmatics and Applied Mathmatics, Hanshan Normal University, Chaozhou, Guangdong 521041, China

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APA Style

Wang Feng, Junmin Zhang. (2013). Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System. Pure and Applied Mathematics Journal, 2(6), 179-183. https://doi.org/10.11648/j.pamj.20130206.12

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ACS Style

Wang Feng; Junmin Zhang. Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System. Pure Appl. Math. J. 2013, 2(6), 179-183. doi: 10.11648/j.pamj.20130206.12

Copy | Download

AMA Style

Wang Feng, Junmin Zhang. Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System. Pure Appl Math J. 2013;2(6):179-183. doi: 10.11648/j.pamj.20130206.12

Copy | Download

@article{10.11648/j.pamj.20130206.12,
  author = {Wang Feng and Junmin Zhang},
  title = {Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System},
  journal = {Pure and Applied Mathematics Journal},
  volume = {2},
  number = {6},
  pages = {179-183},
  doi = {10.11648/j.pamj.20130206.12},
  url = {https://doi.org/10.11648/j.pamj.20130206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.pamj.20130206.12},
  abstract = {By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - Existence of Positive Solution for Fourth Order Superlinear Singular Semipositone Differential System
AU  - Wang Feng
AU  - Junmin Zhang
Y1  - 2013/12/10
PY  - 2013
N1  - https://doi.org/10.11648/j.pamj.20130206.12
DO  - 10.11648/j.pamj.20130206.12
T2  - Pure and Applied Mathematics Journal
JF  - Pure and Applied Mathematics Journal
JO  - Pure and Applied Mathematics Journal
SP  - 179
EP  - 183
PB  - Science Publishing Group
SN  - 2326-9812
UR  - https://doi.org/10.11648/j.pamj.20130206.12
AB  - By transforming the boundary value problem into the corresponding fixed-point problem of a completely continuous operator, the existence is obtained in the paper for two-point boundary value problem of fourth order superlinear singular semipositone differential system via the fixed point theorem concerning cone compression and expansion in norm type.
VL  - 2
IS  - 6
ER  -

Copy | Download