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Zbl 1229.34034
Cabada, Alberto; Cid, José Ángel
Existence and multiplicity of solutions for a periodic Hill's equation with parametric dependence and singularities. (English)
[J] Abstr. Appl. Anal. 2011, Article ID 545264, 19 p. (2011). ISSN 1085-3375; ISSN 1687-0409/e

Summary: We deal with the existence and multiplicity of solutions for the periodic boundary value problem $$x''(t)+a(t)x(t)=\lambda g(t)f(x)+c(t),$$ $$x(0)=x(T),\quad x'(0)=x'(T),$$ where $\lambda$ is a positive parameter. The function $f:(0,\infty)\to (0,\infty)$ is allowed to be singular, and the related Green's function is nonnegative and can vanish at some points.

MSC 2000:: *34B16 Singular nonlinear boundary value problems
34B09 Boundary value problems with an indefinite weight
34B15 Nonlinear boundary value problems of ODE
34B27 Green functions

Keywords: Green's function

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