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On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations. (English) Zbl 1030.34024
Summary: The existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second-order ordinary differential equations. The arguments are based only upon the positivity of Green’s functions and the Krasnosel’skii fixed-point theorem. As an example, a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
74B20Nonlinear elasticity
Full Text: DOI
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[3] Krasnosel’skii, M. A.: Positive solutions of operator equations. (1964)
[4] Jiang, D. Q.: On the existence of positive solutions to second order periodic BVPs. Acta math. Sci. 18, 31-35 (1998)
[5] Rachunková, I.: Existence of two positive solutions of a singular nonlinear periodic boundary value problem. J. comp. Appl. math. 113, 27-34 (2000) · Zbl 0944.34014
[6] Wang, C. C.: On the radial oscillations of a spherical thin shell in the finite elasticity theory. Quart. appl. Math. 23, No. 3, 270-274 (1965)
[7] Wang, J. Y.; Jiang, D. Q.: A singular nonlinear second order periodic boundary value problem. Tohoku math. J. 50, 203-210 (1998) · Zbl 0916.34027
[8] Zhang, M.: Nonuniform nonresonance of semilinear differential equation. J. differential equations 166, 33-50 (2000) · Zbl 0962.34062