바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.19 No.2
Citation Share

EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.2, pp.103-109
https://doi.org/10.7468/jksmeb.2012.19.2.103
Kim, Yong-In
Kim,, Y. (2012). EXISTENCE AND UNIQUENESS OF PERIODIC SOLUTIONS FOR A CLASS OF p-LAPLACIAN EQUATIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(2), 103-109, https://doi.org/10.7468/jksmeb.2012.19.2.103
  • Downloaded
  • Viewed
PDF Download

Abstract

The existence and uniqueness of T-periodic solutions for the following p-Laplacian equations: <TEX>$$({\phi}_p(x^{\prime}))^{\prime}+{\alpha}(t)x^{\prime}+g(t,x)=e(t),\;x(0)=x(T),x^{\prime}(0)=x^{\prime}(T)$$</TEX> are investigated, where <TEX>${\phi}_p(u)={\mid}u{\mid}^{p-2}u$</TEX> with <TEX>$p$</TEX> > 1 and <TEX>${\alpha}{\in}C^1$</TEX>, <TEX>$e{\in}C$</TEX> are T-periodic and <TEX>$g$</TEX> is continuous and T-periodic in <TEX>$t$</TEX>. By using coincidence degree theory, some existence and uniqueness results are obtained.

keywords
p-Laplacian, degree theory, periodic solution

Reference

1.

(2003). Periodic solutions of Lienard equations with asymmetric nonlinearities at resonance. J. London Math. Soc., 68(2), 119-132. 10.1112/S0024610703004459.

2.

(2008). New results of periodic solutions for forced rayleigh-type equations. J. Comput. Appl. Math., 221, 98-105. 10.1016/j.cam.2007.10.005.

3.

(2004). Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument. Nonlinear analysis: TAM, 56, 501-514. 10.1016/j.na.2003.09.021.

4.

(2007). On the existence of periodic solutions to p-Laplacian rayleigh differential equations with a delay. J. Math. Anal. Appl., 325, 685-702. 10.1016/j.jmaa.2006.02.005.

5.

(1998). Periodic solutions for nonlinear systems with p-Laplacian-like operators. J. Diff. Equations, 145, 367-393. 10.1006/jdeq.1998.3425.

6.

(2010). New results of periodic solutions for a kind of forced rayleigh-type equations. Nonlinear Analysis : RWA, 11, 99-105. 10.1016/j.nonrwa.2008.10.018.

7.

(2010). Novel existence and uniqueness criteria for periodic solutions of a Duffing type p-Laplacian equation. Appl. Math. Lett., 23, 436-439. 10.1016/j.aml.2009.11.013.

8.

(2008). Existence and uniqueness of periodic solutions for a kind of Duffing type p-Laplacian equation. Nonlinear Anal. RWA, 9, 985-989. 10.1016/j.nonrwa.2007.01.013.

9.

(1999). Periodic solutions for Rayleigh type p-Laplacian equation with deviating arguments. Appl. Math. Lett., 12, 41-44. 10.1016/S0893-9659(98)00169-4.

10.

(2011). Periodic solutions for a generalized p-Laplacian equation. Appl. Math. Lett., 25, 586-589.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy