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January  2013, 12(1): 451-459. doi: 10.3934/cpaa.2013.12.451

## Multiplicity solutions for fully nonlinear equation involving nonlinearity with zeros

 1 Institute for Advanced Study, Shenzhen University, Shenzhen Guangdong, 518060, China

Received  May 2011 Revised  December 2011 Published  September 2012

We study the multiplicity solutions for the nonlinear elliptic equation

$-\mathcal{M}_{\lambda,\Lambda}^+ (D^2u)=f(u)$ in $\Omega$,

$u=0$ on $\partial \Omega$

and a more general fully nonlinear elliptic equation

$F(D^2u)=f(u)$ in $\Omega$,

$u=0$ on $\partial \Omega$,

where $\Omega$ is a bounded domain in $\mathbb{R}^N, N\geq 3$, $f$ is a locally Lipschitz continuous function with superlinear growth at infinity. We will show that the equation has at least two positive solutions under some assumptions.

Citation: Xiaohui Yu. Multiplicity solutions for fully nonlinear equation involving nonlinearity with zeros. Communications on Pure & Applied Analysis, 2013, 12 (1) : 451-459. doi: 10.3934/cpaa.2013.12.451
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