Mathematical Journal of Ibaraki University

Mathematical Journal of Ibaraki University

Online ISSN : 1883-4353
Print ISSN : 1343-3636
ISSN-L : 1343-3636

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Criterion toward understanding non-constant solutions to p-Laplace Neumann boundary value problem

Kanako Suzuki

Subject area: 2000 Mathematics Subject Classication. 35J57; 35J60; 35B45
2020 Volume 52 Pages 1-13
Published: 2020
Released: November 17, 2020

DOIhttps://doi.org/10.5036/mjiu.52.1

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We consider a p-Laplace equation ∆_pV + h(V) = 0, with an arbitrary C¹-nonlinearity h, in a bounded domain and supplemented with the Neumann boundary condition. We prove a necessary condition for zeros of h = h(V) to be touched by non-constant solutions to this problem.

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Weighted Hardy's inequalities and the variational problem with compact perturbations

Hiroshi Ando, Toshio Horiuchi

Subject area: 2000 Mathematics Subject Classi cation. Primary 35J70, Secondary 35J60, 34L30, 26D10.
2020 Volume 52 Pages 15-26
Published: 2020
Released: November 17, 2020

DOIhttps://doi.org/10.5036/mjiu.52.15

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Let Ω be a bounded domain of ℝ^N(N ≥ 1) whose boundary ∂Ω is a C²compact manifolds. In the present paper we shall study a variational problem relating the weighted Hardy inequalities established in [4]. As weights we adopt powers of the distance function 𝛿(x) to the boundary ∂Ω.

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