Energy–based localization and multiplicity of radially symmetric states for the stationary p–Laplace diffusion. Issue 7 (2nd July 2020)

• Record Type: Journal Article
• Authors: Precup, Radu; Pucci, Patrizia; Varga, Csaba
• Is Part Of: Complex variables and elliptic equations. Volume 65:Issue 7(2020)
• Page Start: 1198
• Page End: 1209
• Publication Date: 2020-07-02
• Subjects: D. Repovš; p–Laplacian -- radial solution -- positive solution -- Harnack inequality -- energy–based localization -- multiple solutions; Primary: 35J20 -- 35J60 -- 34B15 Secondary: 35J15 -- 35J25; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2019.1574774
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: It is investigated the role of the state–dependent source–term for the localization by means of the kinetic energy of radially symmetric states for the stationary p –Laplace diffusion. It is shown that the oscillatory behavior of the source–term, with respect to the state amplitude, yields multiple possible states, located in disjoint energy bands. The mathematical analysis makes use of critical point theory in conical shells and of a version of Pucci–Serrin three–critical point theorem for the intersection of a cone with a ball. A key ingredient is a Harnack type inequality in terms of the energetic norm.