Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian-Reference-Cited by-同舟云学术

Asymptotically Linear Problems and Antimaximum Principle for the Square Root of the Laplacian

Published:2012-11-01 Issue:4 Volume:12 Page:683-701
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Arcoya David¹,Colorado Eduardo²,Leonori Tommaso²

Affiliation:

1. Departamento de Análisis Matemático, Universidad de Granada Facultad de Ciencias, Campus Fuentenueva S/N 18071, Granada, España

2. Departamento de Matemáticas, Universidad Carlos III de Madrid Avda. Universidad 30, 28911 Leganés (Madrid), España

Abstract

Abstract This work deals with bifurcation of positive solutions for some asymptotically linear problems, involving the square root of the Laplacian (−Δ)1/2. A simplified model problem is the following:

with Ω ⊂ ℝN a smooth bounded domain, N ≥ 2, λ > 0, m ∈ L∞ (Ω), m+ ≢ 0 and g is a continuous function which is super-linear at 0 and sub-linear at infinity. As a consequence of our bifurcation theory approach we prove some existence and multiplicity results. Finally, we also show an anti-maximum principle in the corresponding functional setting.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2012-0402/pdf

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