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


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.


Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania

Patrizia Pucci
Dipartimento di Matematica e Informatica, Università degli Studi di Perugia, Perugia, Italy

Csaba Varga
Faculty of Mathematics and Computer Science, Babes–Bolyai University, Cluj–Napoca, Romania; Department of Mathematics, University of Pécs, Pécs, Hungary


p–Laplacian; radial solution; positive solution; Harnack inequality; energy–based localization; multiple solutions.

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R. Precup, P. Pucci, C. Varga,  Energy-based localization and multiplicity of radially symmetric states for the stationary p-Laplace diffusion, Complex Variables and Elliptic Equations 65 (2020):7, 1198-1209,



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Complex Variables and Elliptic Equations
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Taylor and Francis Ltd.

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