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MULTIPLE SOLUTIONS TO p-LAPLACIAN PROBLEMS WITH ASYMPTOTIC NONLINEARITY AS up−1 AT INFINITY

Published online by Cambridge University Press:  06 March 2002

GONGBAO LI  and
HUAN-SONG ZHOU
GONGBAO LI
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071, China; [email protected], [email protected]
HUAN-SONG ZHOU
Affiliation:
Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, PO Box 71010, Wuhan 430071, China; [email protected], [email protected]
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Abstract

The paper studies the existence of multiple solutions to the following p-Laplacian type elliptic problem (p > 1):

where Ω is a bounded domain in ℝN(N [ges ] 1) with smooth boundary ∂Ω, and f(x, u) goes asymptotically in u to [mid ]u[mid ]p−2u at infinity. It is well known that this kind of nonlinear term creates some difficulties in the application of the mountain pass theorem because of the lack of an Ambrosetti–Rabinowitz type superlinear condition on f(x, u). An improved mountain pass theorem is used to prove that the above problem possesses multiple solutions under some natural conditions on f(x, u), and some known results are generalized.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 65 , Issue 1 , February 2002 , pp. 123 - 138
Copyright
2002 London Mathematical Society

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