Existence of Solutions to a Class of Navier Boundary Value Problem Involving the Polyharmonic - Advances in Pure Mathematics

APM > Vol.8 No.4, April 2018

Advances in Pure Mathematics

Volume 8, Issue 4 (April 2018)

ISSN Print: 2160-0368 ISSN Online: 2160-0384

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Existence of Solutions to a Class of Navier Boundary Value Problem Involving the Polyharmonic ()

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DOI: 10.4236/apm.2018.84020 541 Downloads 1,092 Views Citations

Author(s)

Yongyi Lan

Affiliation(s)

School of Sciences, Jimei University, Xiamen, China.

ABSTRACT

This paper is devoted to the following high order elliptic problems under the Navier boundary condition:

Without assuming the standard subcritical polynomial growth condition ensuring the compactness of a bounded (P.S.) sequence, we show that the Navier boundary value problem has at least a weak nontrivial solution for all λ>0 by using mountain pass theorem.

KEYWORDS

Navier Boundary Value Problem, Polyharmonic, Variational Methods, Mountain Pass Theorem

Share and Cite:

Lan, Y. (2018) Existence of Solutions to a Class of Navier Boundary Value Problem Involving the Polyharmonic. Advances in Pure Mathematics, 8, 373-379. doi: 10.4236/apm.2018.84020.

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