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1999 Existence of solutions for a class of semilinear polyharmonic equations with critical exponential growth
Omar Lakkis
Adv. Differential Equations 4(6): 877-906 (1999).

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.

Citation

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Omar Lakkis. "Existence of solutions for a class of semilinear polyharmonic equations with critical exponential growth." Adv. Differential Equations 4 (6) 877 - 906, 1999.

Information

Published: 1999
First available in Project Euclid: 15 April 2013

zbMATH: 0946.35026
MathSciNet: MR1729394

Subjects:
Primary: 35J40
Secondary: 31B30, 35J35, 35J65

Rights: Copyright © 1999 Khayyam Publishing, Inc.

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Vol.4 • No. 6 • 1999
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