Positive solutions for a class of p-Laplace problems involving quasi-linear and semi-linear terms
Autor: | Hongjun Yuan, Mingtao Chen |
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Rok vydání: | 2007 |
Předmět: | |
Zdroj: | Journal of Mathematical Analysis and Applications. 330(2):1179-1193 |
ISSN: | 0022-247X |
DOI: | 10.1016/j.jmaa.2006.08.037 |
Popis: | The aim of this paper is to discuss the positive solutions of the p-Laplace problem − div ( | ∇ u | p − 2 ∇ u ) + g ( u ) | ∇ u | p = λ u q , where p > 1 , q > 1 , g : [ 0 , ∞ ) → [ 0 , ∞ ) is a nonnegative continuous function, λ is a real number. The sufficient condition to have positive solutions of the above problem is g ∈ L 1 ( R + ) . However, if g ∉ L 1 ( R + ) , there is no solution which belongs to it. Therefore, our results are optimal. |
Databáze: | OpenAIRE |
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