American Institute of Mathematical Sciences

Advanced
June  2007, 6(2): 441-451. doi: 10.3934/cpaa.2007.6.441

Positive solutions of semi-Positone Hammerstein integral equations and applications

K. Q. Lan 1,

1. 

Department of Mathematics, Ryerson University, Toronto, Ontario, M5B 2K3, Canada

Received  April 2006 Revised  November 2006 Published  March 2007

Multiple positive solutions for semi-positone Hammerstein integral equations are investigated. This provides a general framework for studying the existence of positive solutions for some semi-positone boundary value problems which can be transferred into the Hammerstein integral equations. We apply the new results on the existence of one or two positive solutions of the semi-positone integral equations to treat the semi-positone conjugate boundary value problems (BVPs) as illustrations although there are many other BVPs which can be treated in the similar way. We provide two explicit examples of semi-positone conjugate BVPs to exhibit applications of our results on the existence of one or two positive solutions.
Keywords: cone., multiple positive solutions, Hammerstein integral equation, Semi-positone, conjugate boundary value problem.
Mathematics Subject Classification: Primary: 34B18; Secondary: 34B15, 34B16, 47H10, 47H3.
Citation: K. Q. Lan. Positive solutions of semi-Positone Hammerstein integral equations and applications. Communications on Pure & Applied Analysis, 2007, 6 (2) : 441-451. doi: 10.3934/cpaa.2007.6.441
[1]

J. R. L. Webb, Gennaro Infante. Semi-positone nonlocal boundary value problems of arbitrary order. Communications on Pure & Applied Analysis, 2010, 9 (2) : 563-581. doi: 10.3934/cpaa.2010.9.563
[2]

K. Q. Lan. Multiple positive eigenvalues of conjugate boundary value problems with singularities. Conference Publications, 2003, 2003 (Special) : 501-506. doi: 10.3934/proc.2003.2003.501
[3]

John R. Graef, Bo Yang. Multiple positive solutions to a three point third order boundary value problem. Conference Publications, 2005, 2005 (Special) : 337-344. doi: 10.3934/proc.2005.2005.337
[4]

John V. Baxley, Philip T. Carroll. Nonlinear boundary value problems with multiple positive solutions. Conference Publications, 2003, 2003 (Special) : 83-90. doi: 10.3934/proc.2003.2003.83
[5]

Xiyou Cheng, Zhaosheng Feng, Zhitao Zhang. Multiplicity of positive solutions to nonlinear systems of Hammerstein integral equations with weighted functions. Communications on Pure & Applied Analysis, 2020, 19 (1) : 221-240. doi: 10.3934/cpaa.2020012
[6]

Gennaro Infante. Positive and increasing solutions of perturbed Hammerstein integral equations with derivative dependence. Discrete & Continuous Dynamical Systems - B, 2020, 25 (2) : 691-699. doi: 10.3934/dcdsb.2019261
[7]

Guglielmo Feltrin. Multiple positive solutions of a sturm-liouville boundary value problem with conflicting nonlinearities. Communications on Pure & Applied Analysis, 2017, 16 (3) : 1083-1102. doi: 10.3934/cpaa.2017052
[8]

Patricio Cerda, Leonelo Iturriaga, Sebastián Lorca, Pedro Ubilla. Positive radial solutions of a nonlinear boundary value problem. Communications on Pure & Applied Analysis, 2018, 17 (5) : 1765-1783. doi: 10.3934/cpaa.2018084
[9]

Christina A. Hollon, Jeffrey T. Neugebauer. Positive solutions of a fractional boundary value problem with a fractional derivative boundary condition. Conference Publications, 2015, 2015 (special) : 615-620. doi: 10.3934/proc.2015.0615
[10]

John R. Graef, Lingju Kong, Min Wang. Existence of multiple solutions to a discrete fourth order periodic boundary value problem. Conference Publications, 2013, 2013 (special) : 291-299. doi: 10.3934/proc.2013.2013.291
[11]

Pasquale Candito, Giovanni Molica Bisci. Multiple solutions for a Navier boundary value problem involving the $p$--biharmonic operator. Discrete & Continuous Dynamical Systems - S, 2012, 5 (4) : 741-751. doi: 10.3934/dcdss.2012.5.741
[12]

Wenming Zou. Multiple solutions results for two-point boundary value problem with resonance. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 485-496. doi: 10.3934/dcds.1998.4.485
[13]

John R. Graef, Lingju Kong, Bo Yang. Positive solutions of a nonlinear higher order boundary-value problem. Conference Publications, 2009, 2009 (Special) : 276-285. doi: 10.3934/proc.2009.2009.276
[14]

John R. Graef, Bo Yang. Positive solutions of a third order nonlocal boundary value problem. Discrete & Continuous Dynamical Systems - S, 2008, 1 (1) : 89-97. doi: 10.3934/dcdss.2008.1.89
[15]

Guglielmo Feltrin. Existence of positive solutions of a superlinear boundary value problem with indefinite weight. Conference Publications, 2015, 2015 (special) : 436-445. doi: 10.3934/proc.2015.0436
[16]

Eric R. Kaufmann. Existence and nonexistence of positive solutions for a nonlinear fractional boundary value problem. Conference Publications, 2009, 2009 (Special) : 416-423. doi: 10.3934/proc.2009.2009.416
[17]

John R. Graef, Johnny Henderson, Bo Yang. Positive solutions to a fourth order three point boundary value problem. Conference Publications, 2009, 2009 (Special) : 269-275. doi: 10.3934/proc.2009.2009.269
[18]

Johnny Henderson, Rodica Luca. Existence of positive solutions for a system of nonlinear second-order integral boundary value problems. Conference Publications, 2015, 2015 (special) : 596-604. doi: 10.3934/proc.2015.0596
[19]

Roman Chapko, B. Tomas Johansson. An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions. Inverse Problems & Imaging, 2008, 2 (3) : 317-333. doi: 10.3934/ipi.2008.2.317
[20]

Lisa Hollman, P. J. McKenna. A conjecture on multiple solutions of a nonlinear elliptic boundary value problem: some numerical evidence. Communications on Pure & Applied Analysis, 2011, 10 (2) : 785-802. doi: 10.3934/cpaa.2011.10.785

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (22)
  • HTML views (0)
  • Cited by (12)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences