Citation: Famei Zheng. Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity[J]. AIMS Mathematics, 2021, 6(2): 1209-1222. doi: 10.3934/math.2021074
[1] | O. Ladyzhenskaja, New equation for the description of incompressible fluids and solvability in the large boundary value of them, P. Steklov I. Math., 102 (19677), 95-118. |
[2] | L. Martinson, K. Pavlov, Magnetohydrodynamics of non-Newtonian fluids, Magnetohydrodynamics, 11 (1975), 47-53. |
[3] | C. Jin, J. Yin, Traveling wavefronts for a time delayed non-Newtonian filtration equation, Physica D, 241 (2012), 1789-1803. doi: 10.1016/j.physd.2012.08.007 |
[4] | Z. Fang, X. Xu, Extinction behavior of solutions for the p-Laplacian equations with nonlocal source, Nonlinear Anal. Real, 13 (2012), 1780-1789. doi: 10.1016/j.nonrwa.2011.12.008 |
[5] | T. Zhou, B. Du, H. Du, Positive periodic solution for indefinite singular Lienard equation with p-Laplacian, Adv. Differ. Equ., 158 (2019), 1-12. |
[6] | S. Ji, J. Yin, R. Huang, Evolutionary p-Laplacian with convection and reaction under dynamic boundary condition, Bound. Value Probl., 194 (2015), 1-12. |
[7] | F. Sanchez-Garduno, P. Maini, Existence and uniqueness of a sharp front travelling wave in degenerate nonlinear diffusion Fisher-KPP equations, J. Math. Biol., 33 (1994), 163-192. doi: 10.1007/BF00160178 |
[8] | Z. Liang, J. Chu, S. Lu, Solitary wave and periodic wave solutions for a non-Newtonian filtration equation, Math. Phys. Anal. Geom., 17 (2014), 213-222. doi: 10.1007/s11040-014-9150-9 |
[9] | F. Kong, Z. Luo, Solitary wave and periodic wave solutions for the non-Newtonian filtration equations with non- linear sources and a time-varying delay, Acta Math. Sci., 37 (2017), 1803-1816. doi: 10.1016/S0252-9602(17)30108-X |
[10] | Z. Liang, F. Kong, Positive periodic wave solutions of singular non-Newtonian filtration equations, Anal. Math. Phys., 7 (2017), 509-524. doi: 10.1007/s13324-016-0153-5 |
[11] | H. Yin, B. Du, Stochastic patch structure Nicholson's blowfies system with mixed delays, Adv. Differ. Equ., 386 (2020), 1-11. |
[12] | H. Yin, B. Du, Q. Yang, F. Duan, Existence of homoclinic orbits for a singular differential equation involving p-Laplacian, J. Funct. Space., 2020 (2020), 1-7. |
[13] | S. Lu, Periodic solutions to a second order p-Laplacian neutral functional differential system, Nonlinear Anal., 69 (2008), 4215-4229. doi: 10.1016/j.na.2007.10.049 |
[14] | W. Ge, J. Ren, An extension of Mawhin's continuation theorem and its application to boundary value problems with a p-Laplacain, Nonlinear Anal., 58 (2004), 477-488. doi: 10.1016/j.na.2004.01.007 |
[15] | R. Hakl, M. Zamora, Periodic solutions to second-order indefinite singular equations, J. Differ. Equations, 263 (2017), 451-469. doi: 10.1016/j.jde.2017.02.044 |
[16] | A. Fonda, A. Sfeccib, On a singular periodic Ambrosetti-Prodi problem, Nonlinear Anal., 19 (2017), 146-155. |
[17] | S. Kumar, D. Kumar, Solitary wave solutions of (3+1)-dimensional extended Zakharov-Kuznetsov equation by Lie symmetry approach, Comput. Math. Appl., 77 (2019), 2096-2113. doi: 10.1016/j.camwa.2018.12.009 |
[18] | D. Kumar, S. Kumar, Some new periodic solitary wave solutions of (3+1)-dimensional generalized shallow water wave equation by Lie symmetry approach, Comput. Math. Appl., 78 (2019), 857-877. doi: 10.1016/j.camwa.2019.03.007 |
[19] | S. Kumar, D. Kumar, Lie symmetry analysis and dynamical structures of soliton solutions for the (2+1)-dimensional modified CBS equation, Int. J. Mod. Phys. B, 34 (2020), 2050221. doi: 10.1142/S0217979220502215 |
[20] | S. Kumar, D. Kumar, Lie symmetry reductions and group Invariant Solutions of (2+1)-dimensional modified Veronese web equation, Nonlinear Dynam., 98 (2019), 1891-1903. doi: 10.1007/s11071-019-05294-x |
[21] | D. Kumar, S. Kumar, Solitary wave solutions of pZK equation using Lie point symmetries, Eur. Phys. J. Plus, 135 (2020), 162. doi: 10.1140/epjp/s13360-020-00218-w |
[22] | S. Kumar, M. Niwas, Lie symmetry analysis, exact analytical solutions and dynamics of solitons for (2+1)-dimensional NNV equations, Phys. Scripta, 95 (2020), 095204. |
[23] | S. Rani, Lie symmetry reductions and dynamics of soliton solutions of (2+1)-dimensional Pavlov equation, Pramana, 19 (2020), 116. |
[24] | S. Kumar, A. Kumar, H. Kharbanda, Lie symmetry analysis and generalized invariant solutions of (2+1)-dimensional dispersive long wave (DLW) equations, Phys. Scripta, 95 (2020), 065207. doi: 10.1088/1402-4896/ab7f48 |
[25] | S. Lu, X. Yu, Periodic solutions for second order differential equations with indefinite singularities, Adv. Nonlinear Anal., 9 (2020), 994-1007. |
[26] | S. Lu, R. Xue, Periodic solutions for a Liénard equation with indefinite weights, Topol. Method. Nonlinear Anal., 54 (2019), 203-218. |
[27] | S. Lu, Y. Guo, L. Chen, Periodic solutions for Liénard equation with an indefinite singularity, Nonlinear Anal. Real, 45 (2019), 542-556. doi: 10.1016/j.nonrwa.2018.07.024 |
[28] | B. Du, S. Lu, On the existence of periodic solutions to a p-Laplacian equation, Indian J. Pure Appl. Math., 40 (2009), 253-266. |
[29] | Y. Xin, Z. Chen, Positive periodic solution for prescribed mean curvature generalized Lienard equation with a singularity, Bound. Value Probl., 89 (2020), 1-15. |