ملخص: We give an extension of application of the homotopy invariance of the topological degree to a problem with jumping nonlinearities of type -u(t)=g(u(t))-[lambda]f(t), u(0)=u(1)=0. 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 [lambda]>0 and [theta][set membership, variant][0,1], which is related to the equation -u=g(u)[theta]+(1-[theta])u2-[lambda](f(t)[theta]+1-[theta]). Then using the homotopy invariance of the topological degree with respect to [theta], on open sets of Zk, for [lambda] large enough, we deduce multiple solutions from the problem -u(t)=u2(t)-[lambda] studied by Ammar Khodja.

لغة: إنجليزية