Taiwanese Journal of Mathematics

NON-TRIVIAL SOLUTIONS FOR $p$-HARMONIC TYPE EQUATIONS VIA A LOCAL MINIMUM THEOREM FOR FUNCTIONALS

Ghasem A. Afrouzi and Armin Hadjian

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Abstract

In this paper, we establish existence results and energy estimatesof weak solutions for an equation involving a $p$-harmonic operator, subject toDirichlet boundary conditions in a bounded smooth open domain of $\mathbb{R}^N$. A critical point result for differentiable functionals is exploited, in order to prove that the problem admits at least one non-trivial weak solution.

Article information

Source
Taiwanese J. Math., Volume 19, Number 6 (2015), 1731-1742.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133736

Digital Object Identifier
doi:10.11650/tjm.19.2015.5542

Mathematical Reviews number (MathSciNet)
MR3434274

Zentralblatt MATH identifier
1357.35117

Subjects
Primary: 35J35: Variational methods for higher-order elliptic equations 35J60: Nonlinear elliptic equations

Keywords
$p$-harmonic operator variational methods critical point

Citation

Afrouzi, Ghasem A.; Hadjian, Armin. NON-TRIVIAL SOLUTIONS FOR $p$-HARMONIC TYPE EQUATIONS VIA A LOCAL MINIMUM THEOREM FOR FUNCTIONALS. Taiwanese J. Math. 19 (2015), no. 6, 1731--1742. doi:10.11650/tjm.19.2015.5542. https://projecteuclid.org/euclid.twjm/1499133736


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