Startseite Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
Artikel
Lizenziert
Nicht lizenziert Erfordert eine Authentifizierung

Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem

  • Ilkay Yaslan Karaca EMAIL logo und Fatma Tokmak Fen
Veröffentlicht/Copyright: 28. April 2017
Veröffentlichen auch Sie bei De Gruyter Brill

Abstract

In this paper, six functionals fixed point theorem is used to investigate the existence of at least three positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem. As an application, we give an example to demonstrate our result.


(Communicated by Michal Fečkan)


References

[1] Agarwal, R. P.—O’regan, D.: Multiple nonnegative solutions for second order impulsive differential equations, Appl. Math. Comput. 114 (2000), 51–59.10.1016/S0096-3003(99)00074-0Suche in Google Scholar

[2] Akhmet, M.: Principles of Discontinuous Dynamical Systems, Springer, New York, 2010.10.1007/978-1-4419-6581-3Suche in Google Scholar

[3] Avery, R.—Henderson, J.—O’Regan, D.: Six functionals fixed point theorem, Commun. Appl. Anal. 12 (2008), 69–81.Suche in Google Scholar

[4] Benchohra, M.—Henderson, J.—Ntouyas, S.: Impulsive Differential Equations and Inclusions, New York, USA, 2006.10.1155/9789775945501Suche in Google Scholar

[5] Fečkan, M.—Zhou, Y.—Wang, J.: On the concept and existence of solution for impulsive fractional differential equations, Commun. Nonlinear Sci. Numer. Simul. 17 (2012), 3050–3060.10.1016/j.cnsns.2011.11.017Suche in Google Scholar

[6] Graef, J. R.—Yang, B.: Positive solutions to a multi-point higher order boundary value problem, J. Math. Anal. Appl. 316 (2006), 409–421.10.1016/j.jmaa.2005.04.049Suche in Google Scholar

[7] Guo, D.: Existence of solutions of boundary value problems for nonlinear second order impulsive differential equations in Banach spaces, J. Math. Anal. Appl. 181 (1994), 407–421.10.1006/jmaa.1994.1031Suche in Google Scholar

[8] Guo, Y.—Shan, W.—Ge, W.: Positive solutions for second-order m-point boundary value problems, J. Comput. Appl. Math. 151 (2003), 415–424.10.1016/S0377-0427(02)00739-2Suche in Google Scholar

[9] Guo, Y.—Ji, Y.—Zhang, J.: Three positive solutions for a nonlinear nth-order m-point boundary value problem, Nonlinear Anal. 68 (2008), 3485–3492.10.1016/j.na.2007.03.041Suche in Google Scholar

[10] 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. 196 (2008), 550–562.10.1016/j.amc.2007.06.014Suche in Google Scholar

[11] Il’in, V. A.—Moiseev, E. I.: A nonlocal boundary value problem of the second kind for the Sturm-Liouville operator, Differentsial’nye Uravneniya 23 (1987), 1422–1431.Suche in Google Scholar

[12] Il’in, V. A.—Moiseev, E. I.: A nonlocal boundary value problem of the first kind for the Sturm-Liouville operator in differential and difference interpretations, Differentsial’nye Uravneniya 23 (1987), 1198–1207.Suche in Google Scholar

[13] Karaca, I. Y.: Positive solutions of an nth order three-point boundary value problem, Rocky Mountain J. Math. 43 (2013), 205–224.10.1216/RMJ-2013-43-1-205Suche in Google Scholar

[14] Lakshmikantham, V.—Bainov, D. D.—Simeonov, P. S.: Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.10.1142/0906Suche in Google Scholar

[15] Liang, S.—Zhang, J.: The existence of countably many positive solutions for some nonlinear singular three-point impulsive boundary value problems, Nonlinear Anal. 71 (2009), 4588–4597.10.1016/j.na.2009.03.016Suche in Google Scholar

[16] Li, P.—Wu, Y.: Triple positive solutions for nth-order impulsive differential equations with integral boundary conditions and p-Laplacian, Results Math. 61 (2012), 401–419.10.1007/s00025-011-0125-xSuche in Google Scholar

[17] Ma, R.: Existence theorem for a second order m-point boundary value problem, J. Math. Anal. Appl. 211 (1997), 545–555.10.1006/jmaa.1997.5515Suche in Google Scholar

[18] Ma, R.: Multiple positive solutions for nonlinear m-point boundary value problems, Appl. Math. Comput. 148 (2004), 249–262.10.1016/S0096-3003(02)00843-3Suche in Google Scholar

[19] Samoilenko, A. M.—Perestyuk, N. A.: Impulsive Differential Equations, World Scientific, Singapore, 1995.10.1142/2892Suche in Google Scholar

[20] Sang, Y. B.—Wei, Z.—Dong, W.: Existence and uniqueness of positive solutions for second-order Sturm-Liouville and multi-point problems on time scales, Bull. Korean Math. Soc. 48 (2011), 1047–1061.10.4134/BKMS.2011.48.5.1047Suche in Google Scholar

[21] Su, H.: Positive solutions for n-order m-point p-Laplacian operator singular boundary value problems, Appl. Math. Comput. 199 (2008), 122–132.10.1016/j.amc.2007.09.043Suche in Google Scholar

[22] Sun, H. R. et al: Existence of solutions for Sturm-Liouville boundary value problem of impulsive differential equations, Abstr. Appl. Anal. (2012), Article ID 707163, 19.10.1155/2012/707163Suche in Google Scholar

[23] Tokmak, F.—Karaca, I. Y.: Existence of symmetric positive solutions for a multipoint boundary value problem with sign-changing nonlinearity on time scales, Bound. Value Probl. 2013:52 (2013), 12.10.1186/1687-2770-2013-52Suche in Google Scholar

[24] Xie, J.—Luo, Z.: Multiple solutions for a second-order impulsive Sturm-Liouville equation, Abstr. Appl. Anal. (2013), Article ID 527082, 6.10.1155/2013/527082Suche in Google Scholar

[25] Xu, F.: Triple positive solutions for higher order m-point p-Laplacian operator boundary value problems, Int. J. Math. Anal. 2 (2008), 863–869.Suche in Google Scholar

[26] Yaslan, I.: Existence of positive solutions for even-order m-point boundary value problems on time scales, Electron. J. Differential Equations 45 (2013), 1–12.Suche in Google Scholar

[27] Zhao, Y. L.—Chen, H. B.—Liu, X. G.: Triple positive solutions of second-order m-point singular boundary value problems, Math. Pract. Theory 41 (2011), 171–177.Suche in Google Scholar

[28] Zhu, Y.—Zhu, J.: Existence of multiple positive solutions for nth-order p-Laplacian m-point singular boundary value problems, J. Appl. Math. Comput. 34 (2010), 393–405.10.1007/s12190-009-0329-3Suche in Google Scholar

Received: 2014-10-16
Accepted: 2015-5-14
Published Online: 2017-4-28
Published in Print: 2017-4-25

© 2017 Mathematical Institute Slovak Academy of Sciences

Artikel in diesem Heft

  1. 10.1515/ms-2015-0200
  2. Zero-divisor graphs of lower dismantlable lattices I
  3. Some results on the intersection graph of submodules of a module
  4. Class number parities of compositum of quadratic function fields
  5. Examples of beurling prime systems
  6. Connection between multiplication theorem for Bernoulli polynomials and first factor hp
  7. On permutational invariance of the metric discrepancy results
  8. Evaluation of sums containing triple aerated generalized Fibonomial coefficients
  9. Linear algebraic proof of Wigner theorem and its consequences
  10. A note on groups with finite conjugacy classes of subnormal subgroups
  11. Groups with the same complex group algebras as some extensions of psl(2, pn)
  12. Klee-Phelps convex groupoids
  13. On analytic functions with generalized bounded Mocanu variation in conic domain with complex order
  14. Weak interpolation for the lipschitz class
  15. Generalized Padé approximants for plane condenser and distribution of points
  16. Three-variable symmetric and antisymmetric exponential functions and orthogonal polynomials
  17. Positive solutions of nonlocal integral BVPS for the nonlinear coupled system involving high-order fractional differential
  18. Existence of positive solutions for a nonlinear nth-order m-point p-Laplacian impulsive boundary value problem
  19. Dirichlet boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses
  20. On the oscillation of certain third order nonlinear dynamic equations with a nonlinear damping term
  21. Homoclinic solutions for ordinary (q, p)-Laplacian systems with a coercive potential
  22. Semi-equivelar maps on the torus and the Klein bottle with few vertices
  23. A problem considered by Friedlander & Iwaniec and the discrete Hardy-Littlewood method
Heruntergeladen am 27.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2016-0282/html
Button zum nach oben scrollen