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OALib Journal期刊
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Multiple positive solutions for equations involving critical Sobolev exponent in R^N

Keywords: Mountain Pass Theorem , Ekeland Variational Principle.

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Abstract:

$$ -{ m div }(|abla u|^{m-2}abla u) = lambda h u^q+u^{m^*-1},quad{ m in}quad R^N,. $$ Using the Ekeland Variational Principle and the Mountain Pass Theorem, we show the existence of $lambda ^*>0$ such that there are at least two non-negative solutions for each $lambda$ in $(0,lambda ^*)$.

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