On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems
On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems
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DOI：
10.1007/s10231-006-0018-x
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发表时间：
2007-07
影响因子：
1
通讯作者：
Nobuyoshi Fukagai;K. Narukawa
中科院分区：
文献类型：
--
作者：
Nobuyoshi Fukagai;K. Narukawa
研究一类具有非齐次主部φ的拟线性椭圆问题$$ \left\{\begin{array}{ll} -\,{\rm div}(\phi(|\nabla u|)\nabla u) = \lambda f(x,u) &\quad\text{in ${\rm \Omega}$} \\ u = 0 &\quad\text{on $\partial{\rm \Omega}$}\end{array}\right.$$。在假设f(x,t)= 0 (φ(t)t) att= 0和∞的条件下，利用Orlicz-Sobolev空间的变分参数证明了问题的多个正解的存在性。
We study a quasilinear elliptic problem $$ \left\{\begin{array}{ll} -\,{\rm div}(\phi(|\nabla u|)\nabla u) = \lambda f(x,u) &\quad\text{in ${\rm \Omega}$} \\ u = 0 &\quad\text{on $\partial{\rm \Omega}$}\end{array}\right.$$ with nonhomogeneous principal part φ. Under the hypothesisf(x,t)=o(φ(t)t) att= 0 and ∞, the existence of multiple positive solutions is proved by using the variational arguments in the Orlicz–Sobolev spaces.