Multiple Solutions for p-Laplacian Type Equations

CHEN Zi-gao

doi:10.13371/j.cnki.chin.q.j.m.2014.03.003

Chinese Quarterly Journal of Mathematics >

2014 , Vol. 29 >Issue 3: 335 - 343

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.03.003

Multiple Solutions for p-Laplacian Type Equations

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Department of Mathematics and Information Science, North China University of Water Resources and Electric Power

CHEN Zi-gao(1978-), male, native of Shangqiu, Henan, an associate professor of North China University of Water Resources and Electric Power, M.S.D., engages in partial differential equations.

Received date: 2013-04-26

Online published: 2020-11-30

Supported by

Supported by the NNSF of China(11101145)； Supported by the NSF of Henan Province(102102210216)；

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Abstract

We establish the existence and multiplicity of weak solutions for equations which involve a uniformly convex elliptic operator in divergence form（in particular, a p-Laplacian operator）, while the nonlinearity has a（p- 1）-superlinear growth at infinity. Our result completes and extends the relevant results of recent papers. The argument in the proof of our main result relies on the Z2-symmetric version of mountain pass lemma.

Key words： variational method; uniformly convex; divergence type operator; symmetric mountain pass lemma

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CHEN Zi-gao . Multiple Solutions for p-Laplacian Type Equations[J]. Chinese Quarterly Journal of Mathematics, 2014 , 29(3) : 335 -343 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.03.003

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