Splitting theorem, Poincare-Hopf theorem and jumping nonlinear problems

摘要

In this paper, we establish a Gromoll-Meyer splitting theorem and a shifting theorem for J is an element of C2-0 (E, R) and by using the finite-dimensional approximation, mollifiers and Morse theory we generalize the Poincare-Hopf theorem to J is an element of C-1 (E, R) case. By combining the Poincare-Hopf theorem and the splitting theorem, we study the existence of multiple solutions for jumping nonlinear elliptic equations. (c) 2004 Elsevier Inc. All rights reserved.