The existence and multiplicity of solutions for second-order impulsive differential equations on the half-line
The authors consider a boundary value problem for impulsive differential equations on the half-line \[ \begin{aligned} -\!u''(t) + u(t) &= \lambda f(t,u(t)) \quad \text{for a.e. } t \in [0,\infty),\\ \triangle u'(t_j) &= I_j(u(t_j)), \quad j = 1,\dotsc,p, \\ u^\prime(0+) &= g(u(0)), \quad u'(\infty) = 0, \end{aligned} \] where \(\lambda > 0\), \(f \in C([0,\infty)\times {\mathbb R};{\mathbb R})\), \(g\), \(I_j \in C({\mathbb R};{\mathbb R})\), \(0 < t_1 < \dotsb < t_p < \infty\). The authors obtain sufficient conditions for the existence of at least one and infinitely many solutions. Variational methods (especially the variant fountain theorem) are used.
scientific article; zbMATH DE number 6135238