Taiwanese Journal of Mathematics

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

Moloud Makvand Chaharlang and Abdolrahman Razani

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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

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

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

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Zentralblatt MATH identifier

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

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


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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