Hostname: page-component-586b7cd67f-2plfb Total loading time: 0 Render date: 2024-11-23T04:46:48.770Z Has data issue: false hasContentIssue false

Non-trivial solutions for a semilinear biharmonic problem with critical growth and potential vanishing at infinity

Published online by Cambridge University Press:  02 April 2015

Yinbin Deng
Affiliation:
Department of Mathematics, Huazhong Normal University, Wuhan 430079, People’s Republic of China, ([email protected])
Wei Shuai
Affiliation:
Department of Mathematics, Huazhong Normal University, Wuhan 430079, People’s Republic of China, ([email protected])

Abstract

In this paper, we study the existence of non-trivial solutions for the following class of semilinear biharmonic problem with critical nonlinearity:

Here Δ 2u = Δ(Δu), N ≥ 5, μ > 0 is a parameter, 2** = 2N/(N − 4) is the critical Sobolev exponent, V (x) and K (x) are positive continuous functions that vanish at infinity, f is a function with a subcritical growth and P(x) is a bounded, non-negative continuous function. By working in weighted Sobolev spaces and using a variational method, we prove that the problem has at least one non-trivial solution.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)