Estimates on the spectral interval of validity of the anti-maximum principle

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:269

Article

Bobkov, Vladimir^1,2  Drabek, Pavel^1,2  Ilyasov, Yavdat³ 

[1] Univ West Bohemia, Fac Appl Sci, Dept Math, Univ 8, Plzen 30100, Czech Republic

[2] Univ West Bohemia, Fac Appl Sci, NTIS, Univ 8, Plzen 30100, Czech Republic

[3] Russian Acad Sci, Ufa Sci Ctr, Inst Math, 112 Chernyshevsky Str, Ufa 450008, Russia

关键词: Anti-maximum principle;    Maximum principle;    p-Laplacian;    Ground state;    Nodal solutions;   

DOI  :  10.1016/j.jde.2020.02.020

来源: Elsevier

【 摘 要 】

The anti-maximum principle for the homogeneous Dirichlet problem to -Delta(p)u =lambda|u|(p-2)u + f(x) with positive f is an element of L-infinity (Omega) states the existence of a critical value lambda(f) > lambda(1) such that any solution of this problem with lambda is an element of(lambda(1), lambda(f)) is strictly negative. In this paper, we give a variational upper bound for lambda(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 (lambda(1), lambda(2)). (c) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free