Taiwanese Journal of Mathematics

A Fourth Order Singular Elliptic Problem Involving $p$-biharmonic Operator

Moloud Makvand Chaharlang and Abdolrahman Razani

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Abstract

In this paper, a fourth order singular elliptic problem involving $p$-biharmonic operator with Dirichlet boundary condition is considered. The existence of at least one weak solution is proved in two different cases of the nonlinear term at the origin. The results are obtained by applying the critical points principle of Ricceri, variational methods and Rellich's inequality. Also an example is presented to verify the results.

Article information

Source
Taiwanese J. Math., Volume 23, Number 3 (2019), 589-599.

Dates
Received: 7 March 2018
Revised: 4 June 2018
Accepted: 18 September 2018
First available in Project Euclid: 26 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1537927424

Digital Object Identifier
doi:10.11650/tjm/180906

Mathematical Reviews number (MathSciNet)
MR3952242

Zentralblatt MATH identifier
07068565

Subjects
Primary: 34B16: Singular nonlinear boundary value problems 35J30: Higher-order elliptic equations [See also 31A30, 31B30] 35J50: Variational methods for elliptic systems

Keywords
singular problem $p$-biharmonic operator variational methods Rellich's inequality

Citation

Makvand Chaharlang, Moloud; Razani, Abdolrahman. A Fourth Order Singular Elliptic Problem Involving $p$-biharmonic Operator. Taiwanese J. Math. 23 (2019), no. 3, 589--599. doi:10.11650/tjm/180906. https://projecteuclid.org/euclid.twjm/1537927424


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References

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