### 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 language | English |
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Journal | Complex Variables and Elliptic Equations |

DOIs | |

Publication status | Published - Jan 1 2019 |

### Fingerprint

### 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

### Cite this

**Energy–based localization and multiplicity of radially symmetric states for the stationary p–Laplace diffusion.** / Precup, Radu; Pucci, Patrizia; Varga, C.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Energy–based localization and multiplicity of radially symmetric states for the stationary p–Laplace diffusion

AU - Precup, Radu

AU - Pucci, Patrizia

AU - Varga, C.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - 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.

AB - 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.

KW - 34B15 Secondary: 35J15

KW - 35J25

KW - 35J60

KW - D. Repovš

KW - energy–based localization

KW - Harnack inequality

KW - multiple solutions

KW - positive solution

KW - Primary: 35J20

KW - p–Laplacian

KW - radial solution

UR - http://www.scopus.com/inward/record.url?scp=85063583598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85063583598&partnerID=8YFLogxK

U2 - 10.1080/17476933.2019.1574774

DO - 10.1080/17476933.2019.1574774

M3 - Article

AN - SCOPUS:85063583598

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

SN - 1747-6933

ER -