Publication Cover
Applicable Analysis
An International Journal
Volume 101, 2022 - Issue 1
282
Views
7
CrossRef citations to date
0
Altmetric
Articles

Sharp conditions for the existence of positive solutions for a second-order singular impulsive differential equation

&
Pages 1-13 | Received 17 Jul 2016, Accepted 15 Aug 2017, Published online: 29 Aug 2017

References

  • Nieto JJ, O’Regan D. Variational approach to impulsive differential equations. Nonlinear Anal. RWA. 2009;10:680–690.
  • Liu X, Willms A. Impulsive controllability of linear dynamical systems with applications to maneuvers of spacecraft. Math Probl Eng. 1996;2:277–99.
  • Pasquero S. Ideality criterion for unilateral constraints in time-dependent impulsive mechanics. J Math Phys. 2005;46:112904.
  • Cushing JM. Periodic time-dependent predator-prey system. SIAM J Appl Math. 1977;32:82–95.
  • Zhang X, Feng M. Transformation techniques and fixed point theories to establish the positive solutions of second-order impulsive differential equations. J Comput Appl Math. 2014;271:117–129.
  • Liu L, Hu L, Wu Y. Positive solutions of two-point boundary value problems for systems of nonlinear second order singular and impulsive differential equations. Nonlinear Anal. 2008;69:3774–3789.
  • Agarwal RP, Franco D, O’Regan D. Singular boundary value problems for first and second order impulsive differential equations. Aequationes Math. 2005;69:83–96.
  • Lin X, Jiang D. Multiple solutions of Dirichlet boundary value problems for second order impulsive differential equations. J Math Anal Appl. 2006;321:501–514.
  • Hu L, Liu L, Wu Y. Positive solutions of nonlinear singular two-point boundary value problems for second-order impulsive differential equations. Appl Math Comput. 2008;196:550–562.
  • Li Q, Cong F, Jiang D. Multiplicity of positive solutions to second order Neumann boundary value problems with impulse actions. Appl Math Comput. 2008;206:810–817.
  • Zhou Q, Jiang D, Tian Y. Multiplicity of positive solutions to period boundary value problems for second order impulsive differential equations. Acta Math Appl Sin-E. 2010;26:113–124.
  • Liu Y, O’Regan D. Multiplicity results using bifurcation techniques for a class of boundary value problems of impulsive differential equations. Commun Nonlinear Sci Numer Simulat. 2011;16:1769–1775.
  • Ma R, Yang B, Wang Z. Positive periodic solutions of first-order delay differential equations with impulses. Appl Math Comput. 2013;219:6074–6083.
  • Hao X, Liu L, Wu Y. Positive solutions for second order impulsive differential equations with integral boundary conditions. Nonlinear Sci Numer Simul. 2011;16:101–111.
  • Lu G, Feng M. Positive Green’s function and triple positive solutions of a second-order impulsive differential equation with integral boundary conditions and a delayed argument. Bound Value Probl. 2016;2016:1–17.
  • Feng M, Qiu J. Multi-parameter fourth order impulsive integral boundary value problems with one-dimensional m-Laplacian and deviating arguments. J Inequal Appl. 2015;2015:1–22.
  • Zhou J, Feng M. Green’s function for Sturm-Liouville-type boundary value problems of fractional order impulsive differential equations and its application. Bound Value Probl. 2014;2014:1–14.
  • Liu X, Guo D. Method of upper and lower solutions for second-order impulsive integro-differential equations in a Banach space. Comput Math Appl. 1999;38:213–223.
  • Pouso R. Necessary and sufficient conditions for existence and uniqueness of solutions of second-order autonomous differential equations. J London Math Soc. 2005;2:397–414.
  • Cid J, Pouso R, Enguiça R. Sharp conditions for the existence of solutions of second-order autonomous differential equations. Mediterr J Math. 2007;42:191–214.
  • Sun J, Chu J. Necessary and sufficient conditions for the existence of periodic solution to singular problems with impulses. Electron J Differ Equ. 2014;98:131–156.
  • Zhang X, Yan J, Zhao A. Existence of positive periodic solutions for an impulsive differential equation. Nonlinear Anal TMA. 2008;68:3209–3216.
  • Guo D, Lakshmikantham V. Nonlinear problems in abstract cones. New York (NY): Academic Press; 1988.
  • Guo D, Lakshmikantham V, Liu X. Nonlinear integral equations in abstract spaces. Dordrecht: Kluwer Academic Publishers; 1996.
  • Zhao Z. Necessary and sufficient condition for the existence of positive solution to a class of singular sub-linear boundary value problems. Acta Math Sin-C. 1998;41:1025–1034.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.