Application of Morse theory for some damped Dirichlet nonlinear impulsive differential equations
The authors consider Dirichlet problem for second order ODE with impulses at fixed times \[ -u''(t) + g(t)u'(t) + \lambda u(t) = f(t,u(t)) \text{ for a.e.}\ t \in [0,T], \] \[ \Delta u'(t_j) = I_j(u(t_j)), \quad j = 1,2,\ldots,p, \] \[ u(0) = u(T) = 0, \] with \(0 < t_1 < t_2 < \cdots < t_p < T\), continuous coefficient \(g\), right-hand side \(f\) and impulse functions \(I_j\). Sufficient conditions ensuring the existence of at least three nontrivial solutions are obtained using Morse theory. Illustrating examples are also given.
scientific article; zbMATH DE number 7491025
scientific article