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EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ ${p}$-LAPLACIAN EQUATIONS

Published online by Cambridge University Press:  23 December 2003

SHIBO LIU  and
SHUJIE LI
SHIBO LIU
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P. R. Chinasliusb@amss.ac.cn
SHUJIE LI
Affiliation:
Institute of Mathematics, Academy of Mathematics and System Sciences, Academia Sinica, Beijing 100080, P. R. Chinaslisj@math03.math.ac.cn
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Abstract

Under very general conditions, a proof is given, via Morse theory, of the existence of solutions for asymptotically ‘linear’ $p$-Laplacian equations, where the asymptotic limit may be greater than the second eigenvalue. The existence of nonzero solutions is also considered.

Keywords

35J6558E05

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Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 1 , January 2004 , pp. 81 - 87
Copyright
© The London Mathematical Society 2004

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