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摘要: 运用Avery-Peterson不动点定理, 研究了三阶三点边值问题 {u‴(t)+λq(t)f(t,u)=0,t∈(0,1),u(0)=αu′(0),u(1)=βu(η),u′(1)=0\eqno3个正解存在的充分条件，其中f:[0,1]×[0,+∞)→[0,+∞)~连续,~λ0~为参数,~0η1,α,β∈R~且~α,β0.
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关键词:
- Avery-Peterson不动点定理
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[1]. [2]problem.Math. Appl. 219(2013)9783-9790. [3]. [4]87-04. [5] Du.Z.J, Ge.W.G, Lin.X.J, Existence of solutions for a class of third-order nonlinear boundary value [6]problems[J].Math. Anal. Appl. 294(2004)104-122. [7] Graef.J.R, Yang.B, Positive solutions of a nonlinear third order eigenvalue problem. Dyn. Syst. Appl. [8](2006)97-110. [9] Feng.Y.Q, Liu.S.Y, Solvability of a third-order two-point boundary value problem. Appl. Math. Lett. [10](2005)1034-1040. [11] Amam.H, Fixed-point equations and nonlinear eigenvalue problems in ordered Banach spaces[J]. [12]SIAM Review.1976.18:620-709. [13] Guo.D, Lakshmikantham.V, Nonlinear Problems in Abstract Cones[M]. New York: Academic Press [14]1988. [15] Leggett.R.W, Williams.L.R., Multiple positive xed points of nonlinear operators on ordered Banach [16]spaces[J].Indiana Univ. Math. J. 1979, 28:673-688.
[1]. [2]problem.Math. Appl. 219(2013)9783-9790. [3]. [4]87-04. [5] Du.Z.J, Ge.W.G, Lin.X.J, Existence of solutions for a class of third-order nonlinear boundary value [6]problems[J].Math. Anal. Appl. 294(2004)104-122. [7] Graef.J.R, Yang.B, Positive solutions of a nonlinear third order eigenvalue problem. Dyn. Syst. Appl. [8](2006)97-110. [9] Feng.Y.Q, Liu.S.Y, Solvability of a third-order two-point boundary value problem. Appl. Math. Lett. [10](2005)1034-1040. [11] Amam.H, Fixed-point equations and nonlinear eigenvalue problems in ordered Banach spaces[J]. [12]SIAM Review.1976.18:620-709. [13] Guo.D, Lakshmikantham.V, Nonlinear Problems in Abstract Cones[M]. New York: Academic Press [14]1988. [15] Leggett.R.W, Williams.L.R., Multiple positive xed points of nonlinear operators on ordered Banach [16]spaces[J].Indiana Univ. Math. J. 1979, 28:673-688.
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