Positive Periodic Solutions to a Second-Order Singular Differential Equation with Indefinite Weights

• Xuefeng Han ^[1] ; Zhibo Cheng ^[1]
  1. [1] Henan Polytechnic University

     Henan Polytechnic University

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • The aim of this paper is to show that Krasnoselskiĭ’s-Guo fixed point theorem can be applied to a second-order singular differential equation with indefinite weights. Using the Green’s function, we prove the existence of a positive periodic solution for the second-order singular differential equation with indefinite weights. These results are applicable to weak as well as strong singularities

• Referencias bibliográficas
  • 1. Chu, J.: On a differential equation arising in geophysics. Monatsh. Math. 187, 499–508 (2018)
  • 2. Huang, J., Ruan, S., Song, J.: Bifurcations in a predator-prey system of Leslie type with generalized Holling type III functional response....
  • 3. Torres, P.: Mathematical models with singularities—a zoo of singular creatures. In: Atlantis Briefs in Differential Equations. Atlantis...
  • 4. Lazer, A., Solimini, S.: On periodic solutions of nonlinear differential equations with singularities. Proc. Am. Math. Soc. 99, 109–114...
  • 5. Cheng, Z., Ren, J.: Periodic solution for second order damped differential equations with attractiverepulsive singularities. Rocky Mount....
  • 6. Chu, J., Fan, N., Torres, P.: Periodic solutions for second order singular damped differential equations. J. Math. Anal. Appl. 388, 665–675...
  • 7. Jiang, D., Chu, J., Zhang, M.: Multiplicity of positive periodic solutions to superlinear repulsive singular equations. J. Differ. Equ....
  • 8. Liu, J., Cheng, Z., Wang, Y.: Positive periodic solution for second-order nonlinear differential equation with singularity of attractive...
  • 9. Torres, P.: Weak singularities may help periodic solutions to exist. J. Differ. Equ. 232, 277–284 (2007)
  • 10. Yu, X., Lu, S.: A multiplicity result for periodic solutions of Liénard equations with an attractive singularity. Appl. Math. Comput....
  • 11. Wang, H.: Positive periodic solutions of singular systems with a parameter. J. Differ. Equ. 249, 2986– 3002 (2010)
  • 12. Bravo, J., Torres, P.: Periodic solutions of a singular equation with indefinite weight. Adv. Nonlinear Stud. 10, 927–938 (2010)
  • 13. Hakl, R., Zamora, M.: Periodic solutions to second-order indefinite singular equations. J. Differ. Equ. 263, 451–469 (2017)
  • 14. Godoy, J., Zamora, M.: A general result to the existence of a periodic solution to an indefinite equation with a weak singularity. J....
  • 15. Cheng, Z., Cui, X.: Positive periodic solution to an indefinite singular equation. Appl. Math. Lett. 112, 106740 (2021)
  • 16. Guo, D., Lakshmikantham, V.: Nonlinear Problems in Abstract Cones. Academic Press, Boston (1988)
  • 17. Torres, P.: Existence of one-signed periodic solutions of some second-order differential equations via a Krasnoselskii fixed point theorem....
  • 18. Hakl, R., Torres, P.: Maximum and antimaximum principles for a second order differential operator with variable coefficients of indefinite...
  • 19. Lomtatidze, A.: Theorems on differential inequalities and periodic boundary value problem for secondorder ordinary differential equations....
  • 20. Han, W., Ren, J.: Some results on second-order neutral functional differential equations with infinite distributed delay. Nonlinear Anal....
  • 21. Cheng, Z., Li, F.: Positive periodic solutions for a kind of second-order neutral differential equations with variable coefficient and...