본문 바로가기
KERD
논문KCI 등재

Existence and Non-Existence of Positive Solutions of BVPsfor Singular ODEs on Whole Lines

0

조회

0

다운로드

0

인용

0

참고문헌

키워드

주제분류수학

초록

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term [Φ(ρ(t)x′(t))]′ involved with the nonnegative singular function ρ and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

Abstract

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term [Φ(ρ(t)x′(t))]′ involved with the nonnegative singular function ρ and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

참고문헌 (22)

  1. R. P. Agarwal, "Boundary value problems for higher order differential equations" (1986), World Scientific
  2. C. Avramescu., "Existence of Homoclinic solutions to a nonlinear second order ODE, Dynamics of continuous, discrete and impulsive systems", Ser. A, Math Anal, 15, pp.481~491 (2008)
  3. C. Avramescu., "Existence of solutions to second order ordinary differential equations having finite limits at 1", Electronic Journal of differential equations, 18, pp.1~12 (2004)
  4. C. Avramescu., "Limits of solutions of a perturbed linear differential equation", E. J. Qualitative Theory of Diff. Equ, 3, pp.1~11 (2002)
  5. A. A. Boichuk., "Dichotomy and boundary value problems on the whole line", Chaotic Modeling and Simulation(CMSIM), 2, pp.247~255 (2013)
  6. B. Bianconi., "Non-autonomous boundary value problems on the real line", Discrete and continuous dynamical systems, 15, pp.759~776 (2006)
  7. A. Calamai, "Heteroclinic solutions of boundary value problems on the real line involving singular Φ-Laplacian operators", Journal of Mathematical Analysis and Applications, 378, pp.667~679 (2011)
  8. A. Cabada., "Heteroclinic solutions for non-autonomous boundary value problems with singular Φ-Laplacian operators, Discrete Contin. Dyn. Syst. , Dynamical Systems, Differential Equations and Applications", 7th AIMS Conference, (suppl), pp.118~122 (2009)
  9. G. Cupini., "Heteroclinic solutions of boundary value problems on the real line involving general nonlinear differential operators", Differ. Integral Equ., 24(7-8), pp.619~644 (2011)
  10. G. Cupini., "On the solvability of a boundary value problem on the real line", Bound. Value Probl, 26, pp.2011~ (2011)
  11. K. Deimling, "Nonlinear Functional Analysis" (1985), Springer
  12. F. Y. Deren., "Second-order boundary-value problems with integral boundary conditions on the real line", Electronic Journal of Differential Equations, 19, pp.1~13 (2014)
  13. W. Ge, "Boundary Value Problems for Ordinary Differential Equations (in Chinese)" (2007), Science Press
  14. V. A. Il’in., "Nonlocal boundary-value problem of the second kind for a Sturm-Liouville operator", Differential Equations, 23, pp.979~987 (1987)
  15. Y. Liu, "Multiple positive solutions to mixed boundary value problems for singular ordinary differential equations on the whole line", Nonlinear Analysis : Modelling and Control, 17(4), pp.460~480 (2012)
  16. Y. Liu, "Existence of multiple positive solutions of p-Laplacian boundary value problems", Math. Slovak, 57, pp.225~242 (2007)
  17. Y. Liu, "Solutions to second order non-homogeneous multi-point BVPs using a fixedpoint theorem", Electronic Journal of Differential Equations, 96, pp.1~52 (2008)
  18. C. Marcelli, "Existence of solutions to some boundary-value problems governed by general nonlinear non-autonomous differential operators", Electron. J. Differ. Equ., 171 (2012)
  19. C. Marcelli, "The role of boundary data on the solvability of some equations involving non-autonomous nonlinear differential operators", Boundary Value Problems, 2013, pp.252~ (2013)
  20. C. Marcelli., "Heteroclinic connections for fully non-linear nonautonomous second-order differential equations", Journal of Differential Equations, 241, pp.160~183 (2007)
  21. K. R. Prasad., "Existence of positive solutions for the system of higher order two-point boundary value problems", Proceedings of the Indian Academy of Sciences Mathematical Sciences, 122, pp.139~152 (2012)
  22. C. G. Philos., "A boundary value problem on the whole line to second order nonlinear differential equations", Georgian Mathematical Journal, 17, pp.241~252 (2010)

관련 논문AI추천

이 간행물의 다른 논문 (21건)