LAUSR

Abstract The paper deals with the boundary value problem for differential equation with ϕ-Laplacian and state-dependent impulses of the form ϕ(z′(t))′=f(t,z(t),z′(t)) for a.e. t∈[0,T]⊂R,Δz′(t)=M(z(t),z′(t−)),t=γ(z(t)),z(0)=z(T)=0. $$\begin{array}{} \left(\phi(z'(t))\right)' = f(t,z(t),z'(t))\qquad \text{ for a.e. } t\in [0,T]\subset\mathbb R,\\ \Delta z'(t) = M(z(t),z'(t-)),\qquad t=\gamma (z(t)),\\ z(0) = z(T) = 0. \end{array} $$ Here, T > 0, ϕ : ℝ → ℝ is an increasing homeomorphism, ϕ(ℝ) = ℝ, ϕ(0) = 0, f : [0, T] × ℝ2 → ℝ satisfies Carathéodory conditions, M : ℝ → ℝ is continuous and γ : ℝ → (0, T) is continuous, Δ z′(t) = z′(t+) − z′(t−). Sufficient conditions for the existence of at least one solution to this problem having no pulsation behaviour are provided.