Existence and nonexistence of positive solutions for nonlinear three-point boundary-value problems

• Autorzy: Yuji L. , Weigao G.
• Języki publikacji: EN

Abstrakty

EN

The authors study the existence and nonexistence of positive solutions to the three point boundary-values problem <fomulas 2> where 0 < Mi < 1 and Beta > 0, a > 0, A > 0. Different conditions for the problem (E) - (B) to hve at least one or two positive solutions and sufficient conditions for this problem to have no positive solutions are given, by applying a new Green's function of three point value problem.

Słowa kluczowe

EN

boundary value problem; positive solution; cone; Green function; fixed point

PL

zagadnienie brzegowe; stożek; funkcja Greena; rozwiązanie dodatnie; punkt stały

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2004
• Tom: Nr 34
• Strony: 157--167
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Yuji L.

• Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P.R. China

autor

Weigao G.

• Department of Mathematics, Yueyang Teacher' College, Hunan, 414000, P.R. China

Bibliografia

• [1] R.P. Agarwal, D. O'Regan, Some new results for singular problem with sign changing nonlinearities, J. of Computational and Applied Mathematics 113(2000), 1-15.
• [2] D.J. Guo, J.X. Sun, Zh.L. Liu, Functional methods for nonlinear ordinary differential equations, Jinan, Shandong Science and Technology Press, 1995 (in Chinese).
• [3] R.Y. Ma, Positive solutions of a nonlinear three-point boundary-value problem, Electronic J. of Differential Equations. 34(1999), 1-8.
• [4] R.Y. Ma, N. Castaneda, Existence of solutions of nonlinear m-point boundary-value problems, J. of Math. Anal. Appl. 256(2001), 556-567.
• [5] R.Y. Ma, Positive solutions for second order three point boundary value problems, Appl. Math. Lett. 14(2001), 1-5.
• [6] R.Y. Ma, Multiplicity of positive solutions for second order three point boundary value problems, Comput. Math. Appl. 40(2000), 193-204.
• [7] J.Y. Wang, D.Q. Jiang, A unified approach to some two-point, three-point, and four-point boundary value problems with Caratheodory functions, J. Math. Anal. Appl. 211(1997), 223-232.