反最大值原理有效谱区间的估计
Estimates on the spectral interval of validity of the anti-maximum principle
摘要：
反最大值原理的齐次狄利克雷问题的$-Δ_p u = λ|u|^{p-2}u + f(x)$与积极的$f \in L^\infty(Ω)$国家的存在一个临界值$λ_f > λ_1$，使任何解决方案的这个问题与$λ\in (λ_1, λ_f)$是严格的负面。本文给出了$λ_f$的一个变分上界，并研究了它的性质.作为一个重要的补充结果，我们研究了$(λ_1,λ_2)$中所考虑的边值问题基态解的分支。
英文摘要：
The anti-maximum principle for the homogeneous Dirichlet problem to $-Δ_p u = λ|u|^{p-2}u + f(x)$ with positive $f \in L^\infty(Ω)$ states the existence of a critical value $λ_f > λ_1$ such that any solution of this problem with $λ\in (λ_1, λ_f)$ is strictly negative. In this paper, we give a variational upper bound for $λ_f$ and study its properties. As an important supplementary result, we investigate the branch of ground state solutions of the considered boundary value problem in $(λ_1,λ_2)$.
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