Energy–based localization and multiplicity of radially symmetric states for the stationary p–Laplace diffusion

Radu Precup, Patrizia Pucci, C. Varga

Research output: Contribution to journalArticle

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.

Original languageEnglish
JournalComplex Variables and Elliptic Equations
DOIs
Publication statusPublished - Jan 1 2019

Keywords

  • 34B15 Secondary: 35J15
  • 35J25
  • 35J60
  • D. Repovš
  • energy–based localization
  • Harnack inequality
  • multiple solutions
  • positive solution
  • Primary: 35J20
  • p–Laplacian
  • radial solution

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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