Existence principle for higher-order nonlinear differential equations with state-dependent impulses via fixed point theorem

Abstract

The paper provides an existence principle for a general boundary value problem of the formn=0 aj(t)u (j) (t )= h(t, u(t), ... , u (n-1) (t)), a.e. t ∈ (a, b) ⊂ R, � k(u, u � , ... , u (n-1) )= ck, k =1 , ... , n, with the state-dependent impulses u (j) (t+) - u (j) (t-) = Jij(u(t-), u � (t-), ... , u (n-1) (t-)), where the impulse points t are determined as solutions of the equations t = γi(u(t-), u � (t-), ... , u (n-2) (t-)), i =1 , ... , p, j =0 , ... , n -1 . Here,n, p ∈ N, c1, ... , cn ∈ R,