Topological degree and a nonlinear Dirichlet problem Original Research Article

We give an extension of application of the homotopy invariance of the topological degree to a problem with jumping nonlinearities of type View the MathML source. To do this, we define sets Zk which are a generalization of sets Sk introduced by Rabinowitz, and calculate a priori estimates. We define a compact operator depending on parameters λ>0 and θ∈[0,1], which is related to the equation View the MathML source. Then using the homotopy invariance of the topological degree with respect to θ, on open sets of Zk, for λ large enough, we deduce multiple solutions from the problem View the MathML source studied by Ammar Khodja.