Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent
Non-homogeneous semilinear elliptic equations involving critical Sobolev exponent
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DOI：
10.1007/s10231-010-0173-y
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发表时间：
2009-12
影响因子：
1
通讯作者：
Y. Naito;Tokushi Sato
中科院分区：
文献类型：
--
作者：
Y. Naito;Tokushi Sato
考虑非齐次临界半线性椭圆问题，其中Ω是一个有界光滑区域，λ > 0是一个参数。我们研究了该问题正解的多重性，发现了依赖于空间维数N的现象。精确地说，我们证明了当κ> 0时，N = 3，4，5和N ≥ 6的情形是完全不同的。我们的证明是基于变分方法和Pohozaev型参数。
We consider the non-homogeneous critical semilinear elliptic problemswhere Ω is a bounded smooth domain ininis a fixed constant, and λ > 0 is a parameter. We investigate the multiplicity of positive solutions to the problem and find the phenomenon depending on the space dimensionN. Precisely, we show that the situation is drastically different between the casesN= 3, 4, 5 andN≥ 6 ifκ> 0. Our proofs are based on the variational methods and Pohozaev type argument.