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Positive solutions for multi-point boundary value problem on the half-line. (English) Zbl 1110.34018
Summary: This paper presents a variety of existence results for nonlinear multipoint boundary value problems on the half-line. In particular, we consider the problem $$x''(t)-px'(t)-qx(t)+f(t,x(t))=0,\quad t\in[0, \infty),$$ $$\alpha x(0)-\beta x'(0)-\sum^n_{i=1}k_i(\xi_i)=a, \quad \lim_{t\to\infty}\frac{x(t)}{e^{rt}}=b,\ r \in\left[0,\frac{p+\sqrt {p^2+4q}}{2}\right].$$ Existence results are established using fixed-point theorems on a cone.

MSC:
34B18Positive solutions of nonlinear boundary value problems for ODE
34B10Nonlocal and multipoint boundary value problems for ODE
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References:
[1] Agarwal, R. P.; O’regan, D.; Wong, P. J. Y.: Positive solutions of differential, difference and integral equations. (1999)
[2] Agarwal, R. P.; O’regan, D.: Infinite interval problems for differential, difference and integral equations. (2001)
[3] Aronson, D.; Crandall, M. G.; Peletier, L. A.: Stabilization of solutions of a degenerate nonlinear diffusion problem. Nonlinear anal. 6, 1001-1022 (1982) · Zbl 0518.35050
[4] Bai, Chuanzhi; Fang, Jinxuan: On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals. J. math. Anal. appl. 282, 711-731 (2003) · Zbl 1036.34075
[5] Baxley, J. V.: Existence and uniqueness of nonlinear boundary value problems on infinite intervals. J. math. Anal. appl. 147, 127-133 (1990) · Zbl 0719.34037
[6] Corduneanu, C.: Integral equations and stability of feedback systems. (1973) · Zbl 0273.45001
[7] Dajun, G.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045
[8] Guo, Yanping; Shan, Wenrui; Ge, Weigao: Positive solutions for second-order m-point boundary value problems. J. comput. Appl. math. 151, 415-424 (2003) · Zbl 1026.34016
[9] Gupta, C. P.; Ntouyas, S. K.; Tsamatos, P. Ch.: Solvablity of an m-point boundary value problem for second-order ordinary differential equations. J. math. Anal. appl. 189, 575-584 (1995) · Zbl 0819.34012
[10] Gupta, C. P.; Trofimchuk, S. I.: A sharper condition for the solvability of a three-point second-order boundary value problem. J. math. Anal. appl. 205, 586-597 (1997) · Zbl 0874.34014
[11] Iffland, G.: Positive solutions of a problem Emden -- Fowler type with a type free boundary. SIAM J. Math. anal. 18, 283-292 (1987) · Zbl 0637.34013
[12] Ilin, V. A.; Moiseev, E. I.: Non-local boundary value problem of the first kind for a Sturm -- Liouville operator in its differential and finite difference aspects. Differ. equ. 23, 803-810 (1987)
[13] Kawano, N.; Yanagida, E.; Yotsutani, S.: Structure theorems for positive radial solutions to $\Delta u+K(|x|)$up=0 in rn. Funkcial. ekvac. 36, 557-579 (1993) · Zbl 0793.34024
[14] Meehan, M.; O’regan, D.: Existence theory for nonlinear Fredholm and Volterra integral equations on half-open intervals. Nonlinear anal. 35, 355-387 (1999) · Zbl 0920.45006
[15] Yan, Baoqiang: Multiple unbounded solutions of boundary value problems for second-order differential equations on the half-line. Nonlinear anal. 51, 1031-1044 (2002) · Zbl 1021.34021
[16] Yan, Baoqiang; Liu, Yansheng: Unbounded solutions of the singular boundary value problems for second-order differential equations on the half-line. Appl. math. Comput. 147, 629-644 (2004) · Zbl 1045.34009
[17] Zima, M.: On positive solution of boundary value problems on the half-line. J. math. Anal. appl. 259, 127-136 (2001) · Zbl 1003.34024