SpringerOpen Newsletter

Receive periodic news and updates relating to SpringerOpen.

Open Access Research

Quasilinear boundary value problem with impulses: variational approach to resonance problem

Pavel Drábek12 and Martina Langerová2*

Author Affiliations

1 Department of Mathematics, University of West Bohemia, Univerzitní 22, Plzeň, 306 14, Czech Republic

2 NTIS, University of West Bohemia, Univerzitní 22, Plzeň, 306 14, Czech Republic

For all author emails, please log on.

Boundary Value Problems 2014, 2014:64  doi:10.1186/1687-2770-2014-64


We dedicate this paper to Professor Ivan Kiguradze for his merits in the theory of differential equations.

Published: 24 March 2014

Abstract

This paper deals with the resonance problem for the one-dimensional p-Laplacian with homogeneous Dirichlet boundary conditions and with nonlinear impulses in the derivative of the solution at prescribed points. The sufficient condition of Landesman-Lazer type is presented and the existence of at least one solution is proved. The proof is variational and relies on the linking theorem.

MSC: 34A37, 34B37, 34F15, 49K35.

Keywords:
quasilinear impulsive differential equations; Landesman-Lazer condition; variational methods; critical point theory; linking theorem