Browse > Article
http://dx.doi.org/10.4134/JKMS.2008.45.6.1549

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)
Publication Information
Journal of the Korean Mathematical Society / v.45, no.6, 2008 , pp. 1549-1559 More about this Journal
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
p-Laplacian equations; periodic solution; one-side Nagumo condition; multiplicity; upper and lower solutions;
Citations & Related Records

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