Existence and Non-Existence of Positive Solutions of BVPsfor Singular ODEs on Whole Lines
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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)
- R. P. Agarwal, "Boundary value problems for higher order differential equations" (1986), World Scientific
- 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)
- 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)
- C. Avramescu., "Limits of solutions of a perturbed linear differential equation", E. J. Qualitative Theory of Diff. Equ, 3, pp.1~11 (2002)
- A. A. Boichuk., "Dichotomy and boundary value problems on the whole line", Chaotic Modeling and Simulation(CMSIM), 2, pp.247~255 (2013)
- B. Bianconi., "Non-autonomous boundary value problems on the real line", Discrete and continuous dynamical systems, 15, pp.759~776 (2006)
- 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)
- 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)
- 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)
- G. Cupini., "On the solvability of a boundary value problem on the real line", Bound. Value Probl, 26, pp.2011~ (2011)
- K. Deimling, "Nonlinear Functional Analysis" (1985), Springer
- 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)
- W. Ge, "Boundary Value Problems for Ordinary Differential Equations (in Chinese)" (2007), Science Press
- V. A. Il’in., "Nonlocal boundary-value problem of the second kind for a Sturm-Liouville operator", Differential Equations, 23, pp.979~987 (1987)
- 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)
- Y. Liu, "Existence of multiple positive solutions of p-Laplacian boundary value problems", Math. Slovak, 57, pp.225~242 (2007)
- 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)
- C. Marcelli, "Existence of solutions to some boundary-value problems governed by general nonlinear non-autonomous differential operators", Electron. J. Differ. Equ., 171 (2012)
- 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)
- C. Marcelli., "Heteroclinic connections for fully non-linear nonautonomous second-order differential equations", Journal of Differential Equations, 241, pp.160~183 (2007)
- 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)
- 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)
