Existence and Multiplicity of Solutions for a Periodic Hill's Equation with Parametric Dependence and Singularities. (7th April 2011) - Cabada, Alberto; Cid, José Ángel
Abstract : We deal with the existence and multiplicity of solutions for the periodic boundary value problemx ″ ( t ) + a ( t ) x ( t ) = λ g ( t ) f ( x ) + c ( t ), x ( 0 ) = x ( T ), x ′ ( 0 ) = x ′ ( T ), whereλ is a positive parameter. The functionf : ( 0, ∞ ) → ( 0, ∞ ) is allowed to be singular, and the related Green's function is nonnegative and can vanish at some points.