Some New Oscillation Criteria for Certain Class of Quasilinear Elliptic Equations
DOI:
https://doi.org/10.26713/cma.v16i1.2908Keywords:
Elliptic equations, Quasilinear, OscillationAbstract
The main goals of this paper is to investigate a new oscillation for a certain class of quasilinear elliptic equations by using Riccati technique. Our main results are demonstrated with an example.
Downloads
References
R. P. Agarwal, S. R. Grace and D. O’Regan, Oscillation Theory for Second Order Linear, Half-Linear, Superlinear and Sublinear Dynamic Equations, 1st edition, Springer, Dordrecht, xiv + 672 pages (2002), DOI: 10.1007/978-94-017-2515-6.
R. P. Agarwal and D. O’Regan, An Introduction to Ordinary Differential Equations, Springer, New York, xii + 321 pages (2008).
W. Allegretto, Oscillation criteria for quasilinear equations, Canadian Journal of Mathematics 26(4) (1974), 931 – 947.
G. E. Chatzarakis, M. Deepa, N. Nagajothi and V. Sadhasivam, Some new oscillation criteria for second-order hybrid differential equations, Hacettepe Journal of Mathematics and Statistics 49 (2020), 1334 – 1345, DOI: 10.15672/hujms.541773.
L. C. Evans, Partial Differential Equations, 2nd edition, Graduate Studies in Mathematics series, Vol. 19, American Mathematical Society, (1998), DOI: 10.1090/gsm/019.
D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, 1st edition, Springer, Berlin — Heidelberg, x + 401 pages (1977), DOI: 10.1007/978-3-642-96379-7.
I. M. Glazman, On the negative part of the spectrum of one-dimensional and multidimensional differential operators over vector-functions, Doklady Akademii Nauk SSSR 119(3) (1958), 421 – 424, URL: https://www.mathnet.ru/eng/dan/v119/i3/p421.
V. B. Headley and C. A. Swanson, Oscillation criteria for elliptic equations, Pacific Journal of Mathematics 27(3) (1968), 501 – 506, URL: https://projecteuclid.org/journals/pacific-journal-ofmathematics/volume-27/issue-3/Oscillation-criteria-for-elliptic-equations/pjm/1102983771.pdf.
J. Jaros, T. Kusano and N. Yoshida, Force superlinear oscillation via Picone’s identity, Acta Mathematica Universitatis Comenianae 69(1) (2000), 107 – 113, URL: http://www.iam.fmph.uniba.sk/amuc/_vol-69/_no_1/_jaros/jaros.html.
K. Kreith, Oscillation theorems for elliptic equations, Proceedings of the American Mathematical Society 15 (1964), 341 – 344, DOI: 10.2307/2034499.
T. Kusano and M. Naito, Oscillation and nonoscillation criteria for second order quasilinear differential equations, Acta Mathematica Hungarica 76(1-2) (1997), 81 – 99, DOI: 10.1007/BF02907054.
E. S. Noussair and C. A. Swanson, Oscillation of semilinear elliptic inequalities by Riccati transformation, Canadian Journal of Mathematics 32(4) (1980), 908 – 923, DOI: 10.4153/CJM-1980-069-8.
Ch. G. Philos, Oscillation theorems for linear differential equations of second order, Archiv der Mathematik 53 (1989), 482 – 492, DOI: 10.1007/BF01324723.
S. Priyadharshini and V. Sadhasivam, Forced oscillation of solutions of conformable hybrid elliptic partial differential equations, Journal Computational Mathematics 6(1) (2022), 396 – 412, DOI: 10.26524/cm140.
S. Pudipeddi, Localized radial solutions for nonlinear p-Laplacian equation in Rn, Electronic Journal of Qualitative Theory of Differential Equations 2008(20) (2008), 1 – 23, DOI: 10.14232/ejqtde.2008.1.20.
S. S. Santra, S. Priyadharshini, V. Sadhasivam, J. Kavitha, U. Fernandez-Gamiz, S. Noeiaghdam and K. M. Khedher, On the oscillation of certain class of conformable Emden-Fowler type elliptic partial differential equations, AIMS Mathematics 8(6) (2023), 12622 – 12636, DOI: 10.3934/math.2023634.
C. A. Swanson, Comparison and Oscillation Theory of Linear Differential Equations, Mathematics in Science and Engineering Series, Vol. 48, Academic Press, New York, (1968).
D. Wei, T. Ji and X. Zhao, Oscillation and non-oscillation criteria for quasi-linear second order differential equations, WSEAS Transactions on Mathematics 11(7) (2008), 627 – 636.
Z. T. Xu, Oscillation and nonoscillation of solutions of second order damped elliptic differential equations, Acta Mathematica Sincia, Chinese Series 47(6) (2004), 1099 – 1106, DOI: 10.12386/A2004sxxb0136. (in Chinese)
N. Yoshida, Oscillation Theory of Partial Differential Equations, World Scientific, (2008), DOI: 10.1142/7046.
N. Yoshida, Forced oscillation criteria superlinear-sublinear elliptic equations via Picone-type inequality, Journal of Mathematical Analysis and Applications 363(2) (2010), 711 – 717, DOI: 10.1016/j.jmaa.2009.10.008.
R. K. Zhuang, Q. R. Wang and S. M. Zhu, Domain oscillation criteria for second order nonlinear elliptic differential equations, Acta Mathematica Sincia, Chinese Series 48(3) (2005), 527 – 534, DOI: 10.12386/A2005sxxb0063. (in Chinese)
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
