Existence and multiplicity of solutions for resonant $(p,2)$-equations

Papageorgiou, Nikolaos S. (avtor), Rǎdulescu, Vicenţiu (avtor), Repovš, Dušan (avtor)

We consider Dirichlet elliptic equations driven by the sum of a $p$-Laplacian $(2 < p)$ and a Laplacian. The conditions on the reaction term imply that the problem is resonant at both $\pm \infty$ and at zero. We prove an existence theorem (producing one nontrivial smooth solution) and a multiplicity theorem (producing five nontrivial smooth solutions, four of constant sign and the fifth nodal; the solutions are ordered). Our approach uses variational methods and critical groups.

• Jezik: Angleški jezik
• Ključne besede: resonance, variational eigenvalues, critical groups, nonlinear regularity, multiple solutions, nodal solutions
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: PEF - Pedagoška fakulteta; FMF - Fakulteta za matematiko in fiziko
• Leto izida: 2018
• Št. strani: Str. 105-129
• Številčenje: Vol. 18, iss. 1
• PID: 20.500.12556/RUL-109142
• UDK: 517.956.2
• ISSN pri članku: 1536-1365
• DOI: 10.1515/ans-2017-0009
• COBISS.SI-ID: 18001241
• Datum objave v RUL: 23.08.2019

PAPAGEORGIOU, Nikolaos S., RǍDULESCU, Vicenţiu in REPOVŠ, Dušan, 2018, Existence and multiplicity of solutions for resonant ▫$(p,2)$▫-equations. Advanced nonlinear studies [na spletu]. 2018. Vol. 18, no. 1, p. 105–129. [Dostopano 4 april 2025]. DOI 10.1515/ans-2017-0009. Pridobljeno s: https://repozitorij.uni-lj.si/IzpisGradiva.php?lang=slv&id=109142

Gradivo je del revije

• Naslov: Advanced nonlinear studies
• Skrajšan naslov: Adv. nonlinear stud.
• Založnik: De Gruyter
• ISSN: 1536-1365
• COBISS.SI-ID: 15060569