论文标题
Orlicz空间中的分数特征值，没有$Δ_2$条件
Fractional eigenvalues in Orlicz spaces with no $Δ_2$ condition
论文作者
论文摘要
我们研究了$ g-$ laplacian操作员的特征值问题，分数顺序Orlicz-sobolev空间，其中$ g = g = g'$，$ g $ and n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n n都无法满足$Δ_2$的条件。我们的主要结果是存在于这种问题的非平凡解决方案。首先证明相应的最小化问题具有解决方案，然后应用广义的Lagrange乘数定理来实现这一点，从而实现这一点。此外，我们证明了特征值的频谱和某些特性的封闭性，并且作为一种应用，我们显示了一类非线性特征值问题的存在。
We study the eigenvalue problem for the $g-$Laplacian operator in fractional order Orlicz-Sobolev spaces, where $g=G'$ and neither $G$ nor its conjugated function satisfy the $Δ_2$ condition. Our main result is the existence of a nontrivial solution to such a problem; this is achieved by first showing that the corresponding minimization problem has a solution and then applying a generalized Lagrange multiplier theorem to get the existence of an eigenvalue. Further, we prove closedness of the spectrum and some properties of the eigenvalues and, as an application, we show existence for a class of nonlinear eigenvalue problems.
