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1996 On quasilinear elliptic equations in $\mathbb{R}^N$
C. O. Alves, J. V. Concalves, L. A. Maia
Abstr. Appl. Anal. 1(4): 407-415 (1996). DOI: 10.1155/S108533759600022X


In this note we give a result for the operator p-Laplacian complementing a theorem by Brézis and Kamin concerning a necessary and sufficient condition for the equation Δu=h(x)uq in N, where 0<q<1, to have a bounded positive solution. While Brézis and Kamin use the method of sub and super solutions, we employ variational arguments for the existence of solutions.


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C. O. Alves. J. V. Concalves. L. A. Maia. "On quasilinear elliptic equations in $\mathbb{R}^N$." Abstr. Appl. Anal. 1 (4) 407 - 415, 1996.


Published: 1996
First available in Project Euclid: 7 April 2003

zbMATH: 0932.35074
MathSciNet: MR1481551
Digital Object Identifier: 10.1155/S108533759600022X

Primary: 35J20 , 35J25

Keywords: $p$-Laplacian , Quasilinear elliptic equation , variational method

Rights: Copyright © 1996 Hindawi

Vol.1 • No. 4 • 1996
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