Lyapunov-type inequalities for a nonlinear system including operators

  • Mustafa Fahri Aktaş Department of Mathematics, Faculty Sciences, Gazi University, Ankara, Turkey
  • Başak Ecem Bingül Department of Mathematics, Faculty Sciences, Gazi University, Ankara, Turkey https://orcid.org/0000-0001-5892-1935
Keywords: Lyapunov-type inequalities, p-relativistic operator, q-prescribed curvature operator

Abstract

UDC 517.9

We obtain new Lyapunov-type inequalities for a nonlinear system including $p$-relativistic operator and $q$-prescribed curvature operator under the Dirichlet or antiperiodic boundary condition.

References

M. F. Aktaş, On Lyapunov-type inequalities for nonlinear Hamiltonian-type problems, Filomat, 36, № 10, 3423–3432 (2022). DOI: https://doi.org/10.2298/FIL2210423A

M. F. Aktaş, On Lyapunov-type inequalities for $(n+1)$st order nonlinear differential equations with the antiperiodic boundary conditions, Turk. J. Math., 45, 2614–2622 (2021). DOI: https://doi.org/10.3906/mat-2006-24

M. F. Aktaş, Periodic solutions of relativistic Liénard-type equations, Electron. J. Qual. Theory Different. Equat., 38, 1–12 (2020). DOI: https://doi.org/10.14232/ejqtde.2020.1.38

M. F. Aktaş, D. Çakmak, A. Tiryaki, Lyapunov-type inequality for quasilinear systems with anti-periodic boundary conditions, J. Math. Inequal., 8, 313–320 (2014). DOI: https://doi.org/10.7153/jmi-08-22

M. F. Aktaş, Lyapunov-type inequalities for $n$-dimensional quasilinear systems, Electron. J. Different. Equat., 67, 1–8 (2013).

M. F. Aktaş, D. Çakmak, A. Tiryaki, A note on Tang and He's paper, Appl. Math. and Comput., 218, 4867–4871 (2012). DOI: https://doi.org/10.1016/j.amc.2011.10.050

D. Çakmak, On Lyapunov-type inequality for a class of quasilinear systems, Electron. J. Qual. Theory Different. Equat., 9, 1–10 (2014). DOI: https://doi.org/10.14232/ejqtde.2014.1.9

D. Çakmak, Lyapunov-type inequalities for two classes of nonlinear systems with anti-periodic boundary conditions, Appl. Math. and Comput., 223, 237–242 (2013). DOI: https://doi.org/10.1016/j.amc.2013.07.099

D. Çakmak, On Lyapunov-type inequality for a class of nonlinear systems, Math. Inequal. Appl., 16, 101–108 (2013). DOI: https://doi.org/10.7153/mia-16-07

D. Çakmak, A. Tiryaki, On Lyapunov-type inequality for quasilinear systems, Appl. Math. and Comput., 216, 3584–3591 (2010). DOI: https://doi.org/10.1016/j.amc.2010.05.004

D. Çakmak, A. Tiryaki, Lyapunov-type inequality for a class of Dirichlet quasilinear systems involving the $(p_{1},p_{2},...,p_{n})$-Laplacian, J. Math. Anal. and Appl., 369, 76–81 (2010). DOI: https://doi.org/10.1016/j.jmaa.2010.02.043

D. Gilbarg, N.S. Trundinger, Elliptic partial differential equations of second order, Springer-Verlag, Berlin, New York (1983).

P. Jebelean, J. Mawhin, C. Serban, Multiple critical orbits to partial periodic perturbations of the $p$-relativistic operator, Appl. Math. Lett., 104, Articl 106220 (2020). DOI: https://doi.org/10.1016/j.aml.2020.106220

P. Jebelean, J. Mawhin, C. Serban, A vector $p$-Laplacian type approach to multiple periodic solutions for the $p$-relativistic operator, Commun. Contemp. Math., 19, 1–16 (2017). DOI: https://doi.org/10.1142/S0219199716500292

P. Jebelean, C. Serban, Boundary-value problems for discontinuous perturbations of singular $phi $-Laplacian operator, J. Math. Anal. and Appl., 431, 662–681 (2015). DOI: https://doi.org/10.1016/j.jmaa.2015.06.004

A. M. Liapunov, Probléme général de la stabilité du mouvement, Ann. Fac. Sci. Univ. Toulouse, 2, 203–407 (1907). DOI: https://doi.org/10.5802/afst.246

I. Sim, Y. H. Lee, Lyapunov inequalities for one-dimensional $p$-Laplacian problems with a singular weight function, J. Inequal. and Appl., 2010, Article ID 865096 (2010). DOI: https://doi.org/10.1155/2010/865096

A. Tiryaki, D. Çakmak, M. F. Aktaş, Lyapunov-type inequalities for two classes of Dirichlet quasilinear systems, Math. Inequal. Appl., 17, 843–863 (2014). DOI: https://doi.org/10.7153/mia-17-62

A. Tiryaki, D. Çakmak, M. F. Aktaş, Lyapunov-type inequalities for a certain class of nonlinear systems, Comput. Math. Appl., 64, 1804–1811 (2012). DOI: https://doi.org/10.1016/j.camwa.2012.02.019

Y. Wang, Lyapunov-type inequalities for certain higher order differential equations with anti-periodic boundary conditions, Appl. Math. Lett., 25, 2375–2380 (2012). DOI: https://doi.org/10.1016/j.aml.2012.07.006

X. J. Wang, Interior gradient estimates for mean curvature equations, Math. Z., 228, 73–81 (1998). DOI: https://doi.org/10.1007/PL00004604

R. Yang, I. Sim, Y. H. Lee, Lyapunov-type inequalities for one-dimensional Minkowski-curvature problems, Appl. Math. Lett., 91, 188–193 (2019). DOI: https://doi.org/10.1016/j.aml.2018.11.006

Published
26.04.2024
How to Cite
AktaşM. F., and BingülB. E. “Lyapunov-Type Inequalities for a Nonlinear System Including Operators”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 76, no. 4, Apr. 2024, pp. 475 -86, doi:10.3842/umzh.v74i4.7374.
Section
Research articles