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