In the present article, we consider a double-phase eigenvalue problem with large exponents. Let λ(pn,qn)1{\lambda }_{\left({p}_{n},{q}_{n})}^{1} be the first eigenvalues and un{u}_{n} be the first eigenfunctions, normalized by ‖un‖ℋn=1\Vert {u}_{n}{\Vert }_{{{\mathcal{ {\mathcal H} }}}_{n}}=1. Under some assumptions on the exponents pn{p}_{n} and qn{q}_{n}, we show that λ(pn,qn)1{\lambda }_{\left({p}_{n},{q}_{n})}^{1} converges to Λ∞{\Lambda }_{\infty } and un{u}_{n} converges to u∞{u}_{\infty } uniformly in the space Cα(Ω){C}^{\alpha }\left(\Omega ), and u∞{u}_{\infty } is a nontrivial viscosity solution to a Dirichlet ∞\infty -Laplacian problem.
在本文中，我们考虑一个具有大指数的双相特征值问题。设 λ ( p n , q n ) 1 {\lambda }_{\left({p}_{n},{q}_{n})}^{1} 为第一特征值，u n {u}_{n} 为第一特征函数，归一化为 ‖ u n ‖ ℋ n = 1 \Vert {u}_{n} {}\Vert }_{{\mathcal{ {\mathcal H} }}_{n}}=1 .}}}_{n}}=1 .在对指数 p n {p}_{n} 和 q n {q}_{n} 有一些假设的情况下 我们证明 λ ( p n , q n ) 1 {\lambda }_{left({p}_{n}、{q}_{n})}^{1} 收敛到 Λ ∞ {Lambda }_{infty }，并且 u n {u}_{n} 收敛到 u ∞ {u}_{infty }，在空间 C α ( Ω ) {C}^{alpha }\left(\Omega ) 中均匀分布、且 u ∞ {u}_{infty } 是一个 Dirichlet ∞ \infty -Laplacian 问题的非微观粘性解。
期刊介绍：
Open Mathematics - formerly Central European Journal of Mathematics
Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant, original and relevant works in all areas of mathematics. The journal provides the readers with free, instant, and permanent access to all content worldwide; and the authors with extensive promotion of published articles, long-time preservation, language-correction services, no space constraints and immediate publication.
Open Mathematics is listed in Thomson Reuters - Current Contents/Physical, Chemical and Earth Sciences. Our standard policy requires each paper to be reviewed by at least two Referees and the peer-review process is single-blind.
Aims and Scope
The journal aims at presenting high-impact and relevant research on topics across the full span of mathematics. Coverage includes:
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
