Existence and multiplicity of solutions for a periodic Hill's equation with parametric dependence and singularities
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.
scientific article; zbMATH DE number 5888139