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Existence and unboundedness of positive solutions for singular boundary value problems on half-line. (English) Zbl 1036.34027
Here, the author gives some existence results on positive solutions to singiular boundary value problems on the half-line for a class of second-order differential equations. He gives also some sufficient conditions to guarantee the boundedness or unboundedness of solutions. The method used is a generalization of a fixed-point theorem in a special cone.

34B16Singular nonlinear boundary value problems for ODE
34B18Positive solutions of nonlinear boundary value problems for ODE
Full Text: DOI
[1] Agarwal, R. P.; O’regan, D.: Second-order boundary value problems of singular type. J. math. Anal. appl. 226, 414-430 (1998) · Zbl 0932.34020
[2] Agarwal, R. P.; O’regan, D.: Nonlinear superlinear singular and nonsingular second order boundary value problems. J. different. Eqs. 143, 60-95 (1998) · Zbl 0902.34015
[3] Lan, K.; Webb, J. L.: Positive solutions of semilinear differential equations with singularities. J. different. Eqs. 148, 407-421 (1998) · Zbl 0909.34013
[4] Liu, X.; Yan, B.: Boundary-irregular solutions to singular boundary value problems. Nonlinear anal. (TMA) 32, 633-646 (1998) · Zbl 0941.34010
[5] Wei, Z.: Positive solutions of singular sublinear second order boundary value problems. Syst. sci. Math. sci. 11, No. 1, 82-88 (1998) · Zbl 0902.34020
[6] Chen, S. Z.; Zhang, Y.: Singular boundary value problems on a half-line. J. math. Anal. appl. 195, 449-468 (1995) · Zbl 0852.34019
[7] Yan, B.: Boundary value problems on the half-line with impulses and infinite delay. J. math. Anal. appl. 259, 94-114 (2001) · Zbl 1009.34059
[8] Guo, D.; Lakshmikantham, V.: Nonlinear problems in abstract cones. (1988) · Zbl 0661.47045
[9] Corduneanu, C.: Integral equations and stability of feedback systems. (1973) · Zbl 0273.45001