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Splitting theorem, Poincaré-Hopf theorem and jumping nonlinear problems |
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| Authors: | Chong Li Shujie Li Jiaquan Liu |
| Affiliation: | a Tsinghua University, Department of Mathematical Sciences, Beijing 100084, P.R. China b Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P.R. China c Institute of Mathematics, Peking University, Beijing 100871, P.R. China |
| Abstract: | In this paper, we establish a Gromoll-Meyer splitting theorem and a shifting theorem for J∈C2-0(E,R) and by using the finite-dimensional approximation, mollifiers and Morse theory we generalize the Poincaré-Hopf theorem to J∈C1(E,R) case. By combining the Poincaré-Hopf theorem and the splitting theorem, we study the existence of multiple solutions for jumping nonlinear elliptic equations. |
| Keywords: | 35J65 58E05 |
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