Advances in Differential Equations

Existence of solutions for a class of semilinear polyharmonic equations with critical exponential growth

Omar Lakkis

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Abstract

The author considers the semilinear elliptic equation $$ -\Delta^{m}u=g(x,u), $$ subject to Dirichlet boundary conditions $u=Du=\cdots=D^{m-1}u=0$, on a bounded domain $\Omega\subset\mathbb{R}^{2m}$. The notion of nonlinearity of critical growth for this problem is introduced. It turns out that the critical growth rate is of exponential type and the problem is closely related to the Trudinger embedding and Moser type inequalities. The main result is the existence of non trivial weak solutions to the problem.

Article information

Source
Adv. Differential Equations Volume 4, Number 6 (1999), 877-906.

Dates
First available in Project Euclid: 15 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.ade/1366030750

Mathematical Reviews number (MathSciNet)
MR1729394

Zentralblatt MATH identifier
0946.35026

Subjects
Primary: 35J40: Boundary value problems for higher-order elliptic equations
Secondary: 31B30: Biharmonic and polyharmonic equations and functions 35J35: Variational methods for higher-order elliptic equations 35J65: Nonlinear boundary value problems for linear elliptic equations

Citation

Lakkis, Omar. Existence of solutions for a class of semilinear polyharmonic equations with critical exponential growth. Adv. Differential Equations 4 (1999), no. 6, 877--906. https://projecteuclid.org/euclid.ade/1366030750.


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