Multiple perturbations of a singular eigenvalue problem

Cencelj, Matija (author), Repovš, Dušan (author), Virk, Žiga (author)

We study the perturbation by a critical term and a ▫$(p-1)$▫-superlinear subcritical nonlinearity of a quasilinear elliptic equation containing a singular potential. By means of variational arguments and a version of the concentration-compactness principle in the singular case, we prove the existence of solutions for positive values of the parameter under the principal eigenvalue of the associated singular eigenvalue problem.

• Language: English
• Keywords: critical Sobolev exponent, indefinite singular potential, principal eigenvalue, concentration-compactness, singularity
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education; FMF - Faculty of Mathematics and Physics
• Year: 2015
• Number of pages: Str. 37-45
• Numbering: Vol. 119
• PID: 20.500.12556/RUL-111406
• UDC: 517.951
• ISSN on article: 0362-546X
• DOI: 10.1016/j.na.2014.07.015
• COBISS.SI-ID: 17086297
• Publication date in RUL: 30.09.2019

Record is a part of a journal

• Title: Nonlinear Analysis
• Shortened title: Nonlinear anal.
• Publisher: Pergamon Press
• ISSN: 0362-546X
• COBISS.SI-ID: 26027520

Secondary language

• Language: Slovenian
• Title: Večkratne perturbacije singularnega problema lastne vrednosti

Abstract

Obravnavamo perturbacijo kritičnega člena in ▫$(p-1)$▫-superlinearno subkritično nelinearnost kvazilinearne eliptične enačbe s singularnim potencialnom. Z variacijskimi argumenti in verzijo principa koncentracijske kompaktnosti v singularnem primeru dokažemo obstoj rešitev za pozitivne vrednosti parametra pod glavno lastno vrednostjo prirejenega singularnega problema lastne vrednosti.

• Keywords: kritični eksponent Soboljeva, nedoločeni singularni potencia, glavna lastna vrednost, koncentracijska kompaktnost, singularnost