DOI QR코드

DOI QR Code

MULTIPLE PERIODIC SOLUTIONS OF p-LAPLACIAN EQUATION WITH ONE-SIDE NAGUMO CONDITION

  • Zhang, Jian Jun (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY) ;
  • Liu, Wen Bin (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY) ;
  • Ni, Jin Bo (DEPARTMENT OF MATHEMATICS ANHUI UNIVERSITY OF SCIENCE AND TECHNOLOGY) ;
  • Chen, Tai Yong (DEPARTMENT OF MATHEMATICS CHINA UNIVERSITY OF MINING AND TECHNOLOGY)
  • Published : 2008.11.01

Abstract

In this paper, the existence and multiplicity of solution of periodic solutions of p-Laplacian boundary value problem are studied by using degree theory and upper and lower solutions method. Some known results are improved.

Keywords

References

  1. K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985
  2. M. Del Pino, M. Elgueta, and R. Manasevich, A homotopic deformation along p of a Leray-Schauder degree result and existence for ($u'^{p-2}{u'}$)′+f(t, u) = 0, u(0) = u(T) = 0, p > 1, J. Differential Equations 80 (1989), no. 1, 1-13 https://doi.org/10.1016/0022-0396(89)90093-4
  3. M. Garcıa-Huidobro, C. P. Gupta, and R. Manasevich, Solvability for a nonlinear threepoint boundary value problem with p-Laplacian-like operator at resonance, Abstr. Appl. Anal. 6 (2001), no. 4, 191-213 https://doi.org/10.1155/S1085337501000550
  4. A. Granas, R. B. Guenther, and J. W. Lee, Some general existence principles in the Caratheodory theory of nonlinear differential systems, J. Math. Pures Appl. (9) 70 (1991), no. 2, 153-196
  5. D. Jiang and W. Gao, Upper and lower solution method and a singular boundary value problem for the one-dimensional p-Laplacian, J. Math. Anal. Appl. 252 (2000), no. 2, 631-648 https://doi.org/10.1006/jmaa.2000.7012
  6. D. Jiang and J. Wang, A generalized periodic boundary value problem for the onedimensional p-Laplacian, Ann. Polon. Math. 65 (1997), no. 3, 265-270 https://doi.org/10.4064/ap-65-3-265-270
  7. L. Lian and W. Ge, The existence of solutions of m-point p-Laplacian boundary value problems at resonance, Acta Math. Appl. Sin. 28 (2005), no. 2, 288-295
  8. B. Liu and J. Yu, Existence of solutions for the periodic boundary value problems with p-Laplacian operator, J. Systems Sci. Math. Sci. 23 (2003), no. 1, 76-85
  9. R. Manasevich and J. Mawhin, Periodic solutions for nonlinear systems with p- Laplacian-like operators, J. Differential Equations 145 (1998), no. 2, 367-393 https://doi.org/10.1006/jdeq.1998.3425
  10. D. O'regan, Some general existence principles and results for ($\phi$(y′))′ = qf(t, y, y′), 0 < t < 1, SIAM J. Math. Anal. 24 (1993), no. 3, 648-668 https://doi.org/10.1137/0524040
  11. I. Rachunkova, Upper and lower solutions and topological degree, J. Math. Anal. Appl. 234 (1999), no. 1, 311-327 https://doi.org/10.1006/jmaa.1999.6375
  12. I. Rachunkova, Upper and lower solutions and multiplicity results, J. Math. Anal. Appl. 246 (2000), no. 2, 446-464 https://doi.org/10.1006/jmaa.2000.6798
  13. X. Yang, Multiple positive solutions of second-order differential equations, Nonlinear Anal. 62 (2005), no. 1, 107-116 https://doi.org/10.1016/j.na.2005.03.013

Cited by

  1. Existence of Solutions of Fractional Differential Equation withp-Laplacian Operator at Resonance vol.2014, 2014, https://doi.org/10.1155/2014/809637
  2. Existence of solutions of two-point boundary value problems for fractional p-Laplace differential equations at resonance vol.41, pp.1-2, 2013, https://doi.org/10.1007/s12190-012-0598-0
  3. Solvability of Some Boundary Value Problems for Fractional -Laplacian Equation vol.2013, 2013, https://doi.org/10.1155/2013/432509
  4. Antiperiodic Solutions for Liénard-Type Differential Equation with -Laplacian Operator vol.2010, pp.1, 2010, https://doi.org/10.1155/2010/194824
  5. Existence criterion for the solutions of fractional order p-Laplacian boundary value problems vol.2015, pp.1, 2015, https://doi.org/10.1186/s13661-015-0425-2
  6. A boundary value problem for fractional differential equation with -Laplacian operator at resonance vol.75, pp.6, 2012, https://doi.org/10.1016/j.na.2011.12.020
  7. Solvability of fractional boundary value problems with p-Laplacian operator vol.2015, pp.1, 2015, https://doi.org/10.1186/s13662-015-0648-7
  8. On the periodic boundary value problem for Duffing type fractional differential equation with p-Laplacian operator vol.2015, pp.1, 2015, https://doi.org/10.1186/s13661-015-0408-3
  9. Some existence results on boundary value problems for fractional p-Laplacian equation at resonance vol.2016, pp.1, 2016, https://doi.org/10.1186/s13661-016-0566-y
  10. Multiple solutions of boundary value problems with ϕ-Laplacian operators and under a Wintner-Nagumo growth condition vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-2770-2013-236
  11. Positive Solutions to Fractional Boundary Value Problems with Nonlinear Boundary Conditions vol.2013, 2013, https://doi.org/10.1155/2013/579740
  12. Solvability of periodic boundary value problem for fractional p-Laplacian equation vol.244, 2014, https://doi.org/10.1016/j.amc.2014.06.105
  13. Existence of positive solutions for fractional differential systems with multi point boundary conditions vol.59, pp.2, 2013, https://doi.org/10.1007/s11565-012-0160-x
  14. Triple positive solutions for a class of two-point boundary-value problems. A fundamental approach vol.189, pp.5, 2013, https://doi.org/10.1007/s10958-013-1222-z