On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting
On principal eigenvalues for quasilinear elliptic differential operators: an Orlicz-Sobolev space setting
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DOI：
10.1007/s000300050073
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发表时间：
1999-05
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通讯作者：
M. García-Huidobro;V. Le;R. Manásevich;K. Schmitt
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作者：
M. García-Huidobro;V. Le;R. Manásevich;K. Schmitt
本文考虑拟线性椭圆型偏微分方程的特征值问题，它是由p-Laplacian的特征值问题所激发的。[3]，[8]，[9]，[19]）。与[10]一样，我们将考虑更一般的问题，这些问题涉及非齐次微分算子。在那里我们考虑了径向函数空间中的边值问题（因此得到了非线性常微分方程的问题），在这里我们考虑一般区域上的问题，并找到一个Orlicz-Sobolev空间（[1]，[15]，[17]）作为该问题的合适框架。将非线性椭圆型方程特征值的存在性问题归结为受约束的强制扩展真实的值泛函（定义在Orlicz-Sobolev空间中）的极小值的存在性问题.然后，本征值的存在将遵循
In this paper we consider eigenvalue problems for quasilinear elliptic partial differential equations which are motivated by eigenvalue problems for the p-Laplacian (cf.[3],[8],[9],[19]). As in [10] we shall consider more general problems, which involve nonhomogeneous differential operators. Whereas there we considered boundary value problems in spaces of radial functions,(and hence obtained problems for nonlinear ordinary differential equations), here we consider the problem on general domains and find an Orlicz-Sobolev space ([1],[15],[17]) setting to be a suitable framework for the problem. We reduce the problem of the existence of eigenvalues of the nonlinear elliptic equation to the question of the existence of a minimum of a coercive extended real valued functional (defined in an Orlicz-Sobolev space) which is subject to a constraint. The existence of the eigenvalue then will follow