We are concerned with Dirichlet problems of the form $$ div(|D u|^{p-2}Du)+f(u)=0 mbox{ in }Omega,qquad u=0 mbox{ on }partialOmega, $$ where $Omega$ is a bounded domain of $R^n$, $nge 2$, $10$ small enough, there exists a unique solution of the Dirichlet problem in the domain $Omega=Omega^Gamma_e={(x_1,x_2)inR^2 : distig((x_1,x_2),Gammaig)2$ and $Omega$ is, for example, a domain of the type $$ Omega=widetildeOmega^Gamma_{e,s}={(x_1,x_2,y) : (x_1,x_2)inOmega^Gamma_e, yinR^{n-2}, |y|

Molle, R., Passaseo, D. (2021). Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 57(2), 535-546 [10.12775/TMNA.2020.048].

Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth

Riccardo Molle
;
2021-06-01

Abstract

We are concerned with Dirichlet problems of the form $$ div(|D u|^{p-2}Du)+f(u)=0 mbox{ in }Omega,qquad u=0 mbox{ on }partialOmega, $$ where $Omega$ is a bounded domain of $R^n$, $nge 2$, $10$ small enough, there exists a unique solution of the Dirichlet problem in the domain $Omega=Omega^Gamma_e={(x_1,x_2)inR^2 : distig((x_1,x_2),Gammaig)2$ and $Omega$ is, for example, a domain of the type $$ Omega=widetildeOmega^Gamma_{e,s}={(x_1,x_2,y) : (x_1,x_2)inOmega^Gamma_e, yinR^{n-2}, |y|
giu-2021
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/05 - ANALISI MATEMATICA
English
Con Impact Factor ISI
Supercritical Dirichlet problems; contractible domains; nonexistence of solutions
The authors have been supported by the “Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA)” of the Istituto Nazionale di Alta Matematica (INdAM) - Project: Equazioni di Schrodinger nonlineari: soluzioni con indice di Morse alto o infinito. The second author acknowledges also the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006.
http://arxiv.org/abs/1912.12243v1
Molle, R., Passaseo, D. (2021). Uniqueness of solutions for nonlinear Dirichlet problems with supercritical growth. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 57(2), 535-546 [10.12775/TMNA.2020.048].
Molle, R; Passaseo, D
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/264578
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