1.School of Data Science and Software Engineering, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China 2.Guangxi Colleges and Universities Key Laboratory of Professional Software Technology, Wuzhou University, Wuzhou 543002, Guangxi Zhuang Autonomous Region, China
Abstract:We investigate the oscillatory behavior of a class of the second-order generalized Emden-Fowler-type differential equations with a nonlinear neutral term the concerned equation is in a noncanonical form, i.e.∫t0+∞a-1/β(t)dt<+∞. By using the generalized Riccati transformation, Bernoulli inequality, Yang inequality and integral averaging technique, we establish some new oscillation criterions for the equations. Two illustrative examples are provided to show that our results extend and improve those reported in the literature, and have practicability and maneuverability.
1 AGARWALR P, BOHNERM, LIW T.Nonoscillation and Oscillation: Theory for Functional Differential Equations[M]. New York: Marcel Dekker, 2004. DOI: 10.1201/9780203025741 2 YANGJ S, WANGJ J, QINX W, et al.Oscillation of nonlinear second-order neutral delay differential equations[J]. Journal of Nonlinear Sciences and Applications, 2017, 10(5): 2727-2734. DOI: 10.1186/s13662-015-0556-x} 3 LIT X, ROGOVCHENKOY V. Oscillation theorems for second-order nonlinear neutral delay differential equations[J]. Abstract and Applied Analysis, 2014(2014): Article ID 594190. DOI: 10.1016/S0898-1221(02)00187-6} 4 LIT, ROGOVCHENKO YUV, TANGS.Oscillation of second-order neutral differential equations with damping [J]. Math Slovaca, 2014, 64 (5): 1227-1236. 5 LINX Y.Oscillation of solutions of neutral differential equations with a super linear neutral term[J]. Applied Mathematics Letters, 2007, 20(9): 1016-1022. DOI: 10.1016/S0898-1221(02)00187-6} 6 SUNS, LIT, HANZ, et al. Oscillation theorems for second-order quasilinear neutral functional differential equations[J]. Abstract and Applied Analysis, 2012, Article ID 819342.doi:10.1155/2012/819342 7 ZHANGC, AGARWALR P, BOHNERM, et al.New oscillation results for second-order neutral delay dynamic equations[J]. Advances in Difference Equations, 2012(1): 227. DOI: 10.1016/S0096-3003(02)00286-2 8 AGARWALR P,BOHNERM, LIT X,et al.Oscillation of second-order Emden–Fowler neutral delay differential equations[J]. Annali di Matematica Pura ed Applicata, 2014, 193(6): 1861-1875. DOI: 10.1007/s10231-013-0361-7 9 AGARWALR P, BOHNERM, LIT, et al.Oscillation of second-order differential equations with a sublinear neutral term[J]. Carpathian Journal of Mathematics, 2014, 30(1):1-6. DOI: 10.1016/j.amc.2004.04.017 10 HANZ, LIT, SUNS, et al.Remarks on the paper [J]. Appl Math Comput, 2010, 215: 3998-4007. DOI: 10.1016/j.amc.2009.12.006 11 HUANGJ Z,FUC H.Oscillation criteria of generalized Emden-Fowler equations[J].Acta Mathematicae Applicatae Sinica,2015,38(6): 1126-1135. 12 ZENGY H,LUOL P,YUY H.Oscillation for Emden-Fowler delay differential equations of neutral type[J].Acta Mathematica Scientia, 2015, 35(4): 803-814. DOI:10.3969/j.issn.1003-3998.2015.04.016 13 YANGJ S, FANGB.Oscillation of certain second-order generalized Emden-Fowler--type differential equations[J].Journal of Central China Normal University (Natural Sciences),2016,50(6):799-804. DOI:10.3969/j.issn.1000-1190.2016.06.001 14 YUQ,YANGJ S.Oscillation analysis of second-order nonlinear variable delay neutral differential equations[J].Journal of Anhui University (Natural Science Edition), 2016,40(4):22-29. DOI:10.3969/j.issn.1000-2162.2016.04.005 15 YANGJ S,QING J.Kamenev-type oscillation criteria for certain second-order differential equations[J].Journal of Zhejiang University (Science Edition), 2017,44(3):274-280. DOI:10.3785/j.issn.1008-9497.2017.03.005 16 YANGJ S.Oscillation of certain second-order nonlinear neutral functional differential equations with variable delay[J]. Journal of Zhejiang University (Science Edition), 2016,43(3):257-263. DOI:10.3785/j.issn.1008-9497.2016.03.002 17 YANGJiashan.Oscillation of second-order variable delay differential equations with nonlinear neutral term[J].Journal of East China Normal University (Natural Science),2016, 2016(4): 30-37. DOI:10.3969/j.issn.1000-5641.2016.04.004 18 YANGJ S.Oscillation criteria of second-order Emden-Fowler nonlinear variable delay differential equations[J].Journal of Zhejiang University (Science Edition),2017,44(2):144-149. DOI:10.3785/j.issn.1008-9497.2017.02.004 19 YANGJ S, ZHANGX J.Oscillation of second order damped differential equation with positive and negative coefficients[J]. Applied Mathematics A Journal of Chinese Universities(Ser A), 2011, 26(4): 399-406. DOI:10.3969/j.issn.1000-4424.2011.04.003 20 YANGJ S.Oscillation of solutions for a class of second-order nonlinear variable delay difference equation[J]. Journal of Yantai University(Natural Science and Engineering Edition), 2012,25(2):90-94. DOI:10.3969/j.issn.1004-8820.2012.02.004 21 BOHNERM,LIT X.Kamenev-type criteria for nonlinear damped dynamic equations[J].Science China Mathematics,2015,58(7):1445- 1452. DOI: 10.1007/s11425-015-4974-8