×

Existence of periodic solutions for \(p\)-Laplacian equations on time scales. (English) Zbl 1195.34139

Summary: Sufficient criteria are established for the existence of periodic solutions. The main method is based on Mawhin’s continuation theorem.

MSC:

34N05 Dynamic equations on time scales or measure chains
34C25 Periodic solutions to ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Lu S:Existence of periodic solutions to a[InlineEquation not available: see fulltext.]-Laplacian Liénard differential equation with a deviating argument.Nonlinear Analysis: Theory, Methods & Applications 2008,68(6):1453-1461. 10.1016/j.na.2006.12.041 · Zbl 1139.34316 · doi:10.1016/j.na.2006.12.041
[2] Xiao B, Liu B:Periodic solutions for Rayleigh type[InlineEquation not available: see fulltext.]-Laplacian equation with a deviating argument.Nonlinear Analysis: Real World Applications 2009,10(1):16-22. 10.1016/j.nonrwa.2007.08.010 · Zbl 1154.34373 · doi:10.1016/j.nonrwa.2007.08.010
[3] Gaines RE, Mawhin JL: Coincidence Degree, and Nonlinear Differential Equations, Lecture Notes in Mathematics. Volume 568. Springer, Berlin, Germany; 1977:i+262.
[4] Cheung WS, Ren JL:On the existence of periodic solutions for[InlineEquation not available: see fulltext.]-Laplacian generalized Liénard equation.Nonlinear Analysis: Theory, Methods & Applications 2005,60(1):65-75. · Zbl 1066.34074
[5] Zhang FX, Li Y:Existence and uniqueness of periodic solutions for a kind of Duffing type[InlineEquation not available: see fulltext.]-Laplacian equation.Nonlinear Analysis: Real World Applications 2008,9(3):985-989. 10.1016/j.nonrwa.2007.01.013 · Zbl 1167.34344 · doi:10.1016/j.nonrwa.2007.01.013
[6] Liu B:Existence and uniqueness of periodic solutions for a kind of Liénard type[InlineEquation not available: see fulltext.]-Laplacian equation.Nonlinear Analysis: Theory, Methods & Applications 2008,69(2):724-729. 10.1016/j.na.2007.06.007 · Zbl 1161.34022 · doi:10.1016/j.na.2007.06.007
[7] Manásevich R, Mawhin J:Periodic solutions for nonlinear systems with[InlineEquation not available: see fulltext.]-Laplacian-like operators.Journal of Differential Equations 1998,145(2):367-393. 10.1006/jdeq.1998.3425 · Zbl 0910.34051 · doi:10.1006/jdeq.1998.3425
[8] Cao FJ, Han ZL:Existence of periodic solutions for[InlineEquation not available: see fulltext.]-Laplacian differential equation with deviating arguments.Journal of Uuniversity of Jinan (Science & Technology) 2010, 24: 1-4.
[9] Hilger S: Analysis on measure chains-a unified approach to continuous and discrete calculus.Results in Mathematics 1990,18(1-2):18-56. · Zbl 0722.39001 · doi:10.1007/BF03323153
[10] Bohner M, Peterson A: Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser, Boston, Mass, USA; 2001:x+358. · Zbl 0978.39001 · doi:10.1007/978-1-4612-0201-1
[11] Bohner M, Peterson A: Advances in Dynamic Equations on Time Scales. Birkhäuser, Boston, Mass, USA; 2003:xii+348. · Zbl 1025.34001 · doi:10.1007/978-0-8176-8230-9
[12] Kaufmann ER, Raffoul YN: Periodic solutions for a neutral nonlinear dynamical equation on a time scale.Journal of Mathematical Analysis and Applications 2006,319(1):315-325. 10.1016/j.jmaa.2006.01.063 · Zbl 1096.34057 · doi:10.1016/j.jmaa.2006.01.063
[13] Bohner M, Fan M, Zhang JM: Existence of periodic solutions in predator-prey and competition dynamic systems.Nonlinear Analysis: Real World Applications 2006,7(5):1193-1204. 10.1016/j.nonrwa.2005.11.002 · Zbl 1104.92057 · doi:10.1016/j.nonrwa.2005.11.002
[14] Li YK, Zhang HT: Existence of periodic solutions for a periodic mutualism model on time scales.Journal of Mathematical Analysis and Applications 2008,343(2):818-825. 10.1016/j.jmaa.2008.02.002 · Zbl 1146.34326 · doi:10.1016/j.jmaa.2008.02.002
[15] Liu XL, Li WT: Periodic solutions for dynamic equations on time scales.Nonlinear Analysis: Theory, Methods & Applications 2007,67(5):1457-1463. 10.1016/j.na.2006.07.030 · Zbl 1124.34028 · doi:10.1016/j.na.2006.07.030
[16] Bohner M, Fan M, Zhang JM: Periodicity of scalar dynamic equations and applications to population models.Journal of Mathematical Analysis and Applications 2007,330(1):1-9. 10.1016/j.jmaa.2006.04.084 · Zbl 1179.34106 · doi:10.1016/j.jmaa.2006.04.084
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.